A Comparison of Procedures for Controlling the False Discovery Rate in the Presence of Small Variance Genes: A Simulation Study

The Significance Analysis of Microarrays (SAM; Tusher et al., 2001 Tusher , V. G. , Tibshirani , R. , Chu , G. ( 2001 ). Significance analysis of microarrys applied to the ionizing radiation response . Proceedings of the National Academy of Sciences 98 : 5116 – 5121 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) method is widely used in analyzing gene expression data while controlling the FDR by using resampling-based procedure in the microarray setting. One of the main components of the SAM procedure is the adjustment of the test statistic. The introduction of the fudge factor to the test statistic aims at deflating the large value of test statistics due to the small standard error of gene-expression. Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) pointed out that the fudge factor does not effectively improve the power and the control of the FDR as compared to the SAM procedure without the fudge factor in the presence of small variance genes. Motivated by the simulation results presented in Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), in this article, we extend our study to compare several methods for choosing the fudge factor in the modified t-type test statistics and use simulation studies to investigate the power and the control of the FDR of the considered methods.     

On Complete Convergence for Arrays of Dependent Random Variables

A complete convergence theorem for an array of rowwise independent random variables was established by Sung et al. (2005 Sung , S. H. , Volodin , A. I. , Hu , T.-C. ( 2005 ). More on complete convergence for arrays . Statist. Probab. Lett. 71 : 303 – 311 .[Crossref], [Web of Science ®] , [Google Scholar]). This result has been generalized and extended by Kruglov et al. (2006 Kruglov , V. M. , Volodin , A. I. , Hu , T.-C. ( 2006 ). On complete convergence for arrays . Statist. Probab. Lett. 76 : 1631 – 1640 .[Crossref], [Web of Science ®] , [Google Scholar]) and Chen et al. (2007 Chen , P. , Hu , T.-C. , Liu , X. , Volodin , A. ( 2007 ). On complete convergence for arrays of rowwise negatively associated random variables . Theor. Probab. Appl. 52 : 393 – 397 . [Google Scholar]). In this article, we extend the results of Sung et al. (2005 Sung , S. H. , Volodin , A. I. , Hu , T.-C. ( 2005 ). More on complete convergence for arrays . Statist. Probab. Lett. 71 : 303 – 311 .[Crossref], [Web of Science ®] , [Google Scholar]), Kruglov et al. (2006 Kruglov , V. M. , Volodin , A. I. , Hu , T.-C. ( 2006 ). On complete convergence for arrays . Statist. Probab. Lett. 76 : 1631 – 1640 .[Crossref], [Web of Science ®] , [Google Scholar]), and Chen et al. (2007 Chen , P. , Hu , T.-C. , Liu , X. , Volodin , A. ( 2007 ). On complete convergence for arrays of rowwise negatively associated random variables . Theor. Probab. Appl. 52 : 393 – 397 . [Google Scholar]) to an array of dependent random variables satisfying Hoffmann-Jørgensen type inequalities.     

A Generalization of the Skew-Normal Distribution: The Beta Skew-Normal

We consider a new generalization of the skew-normal distribution introduced by Azzalini (1985 Azzalini , A. ( 1985 ). A class of distributions which includes the normal ones . Scand. J. Statis. 12 ( 2 ): 171 – 178 .[Web of Science ®] , [Google Scholar]). We denote this distribution Beta skew-normal (BSN) since it is a special case of the Beta generated distribution (Jones, 2004 Jones , M. C. ( 2004 ). Families of distributions of order statistics . Test 13 ( 1 ): 1 – 43 .[Crossref], [Web of Science ®] , [Google Scholar]). Some properties of the BSN are studied. We pay attention to some generalizations of the skew-normal distribution (Bahrami et al., 2009 Bahrami , W. , Agahi , H. , Rangin , H. ( 2009 ). A two-parameter Balakrishnan skew-normal distribution . J. Statist. Res. Iran 6 : 231 – 242 . [Google Scholar]; Sharafi and Behboodian, 2008 Sharafi , M. , Behboodian , J. ( 2008 ). The Balakrishnan skew-normal density . Statist. Pap. 49 : 769 – 778 .[Crossref], [Web of Science ®] , [Google Scholar]; Yadegari et al., 2008 Yadegari , I. , Gerami , A. , Khaledi , M. J. ( 2008 ). A generalization of the Balakrishnan skew-normal distribution . Statist. Probab. Lett. 78 : 1165 – 1167 .[Crossref], [Web of Science ®] , [Google Scholar]) and to their relations with the BSN.     

The Identification of Potential Longitudinal Biomarkers and Measurements of Effectiveness for Biomarkers as Surrogates in Multivariate Survival Data

A proposed method based on frailty models is used to identify longitudinal biomarkers or surrogates for a multivariate survival. This method is an extention of earlier models by Wulfsohn and Tsiatis (1997 Wulfsohn , M. S. , Tsiatis , A. A. ( 1997 ). A joint model for survival and longitudinal data measured with error . Biometrics 53 ( 1 ): 330 – 339 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Song et al. (2002 Song , X. , Davidian , M. , Tsiatis , A. A. ( 2002 ). A Semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data . Biometrics 58 ( 4 ): 742 – 753 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). In this article, similar to Henderson et al. (2002 Henderson , R. , Diggle , P. J. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), a joint likelihood function combines the likelihood functions of the longitudinal biomarkers and the multivariate survival times. We use simulations to explore how the number of individuals, the number of time points per individual and the functional form of the random effects from the longitudianl biomarkers influence the power to detect the association of a longitudinal biomarker and the multivariate survival time. The proposed method is illustrate by using the gastric cancer data.     

Is Each NPMLE of a Continuous Bivariate Distribution Function with Singly Right-Censored Data Really Inconsistent?

We consider non-parametric estimation of a continuous cdf of a random vector (X ₁, X ₂). With bivariate RC data, it is stated in van der Laan (1996 Van der Laan , M. J. ( 1996 ) Efficient estimation in the bivariate censoring model and repairing NPMLE . Ann. Statist. 24 : 596 – 627 .[Crossref], [Web of Science ®] , [Google Scholar], p. 598¹⁰, Ann. Statist.), Quale et al. (2006 Quale , C. M. , van der Laan , M. J. , Robins , J. R. ( 2006 ). Locally efficient estimation with bivariate right-censored data . JASA. 101 : 1076 – 1084 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], JASA) etc. that “it is well known that the NPMLE for continuous data is inconsistent (Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar])).” The claim is based on a result in Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], p.1352, Ann. Statist.) that if X ₁ is right censored but not X ₂, then common ways for defining one NPMLE lead to inconsistency. If X ₁ is right censored and X ₂ is type I right-censored (which includes the case in Tsai et al.), we present a consistent NPMLE. The result corrects a common misinterpretation of Tsai's example (Tsai et al., 1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], Ann. Statist.).     

Aspects of Dependence in Generalized Farlie-Gumbel-Morgenstern Distributions

In this article, we obtained a dependence measure for generalized Farlie-Gumbel-Morgenstern (FGM) family in view of Kochar and Gupta (1987 Kochar , S. G. , Gupta , R. P. ( 1987 ). Competitors of Kendall-tau test for testing independence against PQD . Biometrika 74 ( 3 ): 664 – 669 .[Crossref], [Web of Science ®] , [Google Scholar]) and then compared this measure with Spearman's rho and Kendall's tau in FGM family. Moreover, we evaluated the empirical power of the class of distribution-free tests proposed by Kochar and Gupta (1987 Kochar , S. G. , Gupta , R. P. ( 1987 ). Competitors of Kendall-tau test for testing independence against PQD . Biometrika 74 ( 3 ): 664 – 669 .[Crossref], [Web of Science ®] , [Google Scholar], 1990 Kochar , S. G. , Gupta , R. P. ( 1990 ). Distribution-free tests based on sub-sample extrema for testing against positive dependence . Australian Journal of Statistics 32 : 45 – 51 .[Crossref] , [Google Scholar]) based on exact distribution of a U-statistics. This is derived via a simulation study for sample of sizes n = 6, 8, 10, 12, 16, and 20. Also, we compared our simulation results with those achieved by Amini et al. (2010 Amini , M. , Jabbari , H. , Mohtashami Borzadaran , G. R. , Azadbakhsh , M. ( 2010 ). Power comparison of independence test for the Farlie-Gumbel-Moregenstern family . Communications of the Korean Statistical Society 17 ( 4 ): 493 – 505 .[Crossref] , [Google Scholar]) and Güven and Kotz (2008 Güven , B. , Kotz , S. ( 2008 ). Test of independence for generalized Farlie-Gumbel-Morgenstern distributions . Journal of Computational and Applied Mathematics 212 : 102 – 111 .[Crossref], [Web of Science ®] , [Google Scholar]).     

The Performance of Panel Cointegration Methods: Results from a Large Scale Simulation Study

This article presents results concerning the performance of both single equation and system panel cointegration tests and estimators. The study considers the tests developed in Pedroni (1999 Pedroni , P. ( 1999 ). Critical values for cointegration tests in heterogeneous panels with multiple regressors . Oxford Bulletin of Economics and Statistics 61 : 653 – 670 .[Crossref], [Web of Science ®] , [Google Scholar], 2004 Pedroni , P. ( 2004 ). Panel cointegration. Asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis . Econometric Theory 20 : 597 – 625 .[Crossref], [Web of Science ®] , [Google Scholar]), Westerlund (2005 Westerlund , J. ( 2005 ). New simple tests for panel cointegration . Econometric Reviews 24 : 297 – 316 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Larsson et al. (2001 Larsson , R. , Lyhagen , J. , Löthgren , M. ( 2001 ). Likelihood-based cointegration tests in heterogeneous panels . Econometrics Journal 4 : 109 – 142 .[Crossref] , [Google Scholar]), and Breitung (2005 Breitung , J. ( 2005 ). A parametric approach to the estimation of cointegration vectors in panel data . Econometric Reviews 24 : 151 – 173 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and the estimators developed in Phillips and Moon (1999 Phillips , P. C. B. , Moon , H. R. ( 1999 ). Linear regression limit theory for nonstationary panel data . Econometrica 67 : 1057 – 1111 .[Crossref], [Web of Science ®] , [Google Scholar]), Pedroni (2000 Pedroni , P. ( 2000 ). Fully modified OLS for heterogeneous cointegrated panels . In: Baltagi , B. H. , ed. Nonstationary Panels, Panel Cointegration, and Dynamic Panels . Amsterdam : Elsevier , pp. 93 – 130 .[Crossref] , [Google Scholar]), Kao and Chiang (2000 Kao , C. , Chiang , M.-H. ( 2000 ). On the estimation and inference of a cointegrated regression in panel data . In: Baltagi , B. H. , ed. Nonstationary Panels, Panel Cointegration, and Dynamic Panels . Amsterdam : Elsevier , pp. 179 – 222 .[Crossref] , [Google Scholar]), Mark and Sul (2003 Mark , N. C. , Sul , D. ( 2003 ). Cointegration vector estimation by panel dynamic OLS and long-run money demand . Oxford Bulletin of Economics and Statistics 65 : 655 – 680 .[Crossref], [Web of Science ®] , [Google Scholar]), Pedroni (2001 Pedroni , P. ( 2001 ). Purchasing power parity tests in cointegrated panels . Review of Economics and Statistics 83 : 1371 – 1375 . [Google Scholar]), and Breitung (2005 Breitung , J. ( 2005 ). A parametric approach to the estimation of cointegration vectors in panel data . Econometric Reviews 24 : 151 – 173 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). We study the impact of stable autoregressive roots approaching the unit circle, of I(2) components, of short-run cross-sectional correlation and of cross-unit cointegration on the performance of the tests and estimators. The data are simulated from three-dimensional individual specific VAR systems with cointegrating ranks varying from zero to two for fourteen different panel dimensions. The usual specifications of deterministic components are considered.     

Using Frailty Models to Identify the Longitudinal Biomarkers in Survival Analysis

We introduce a score test to identify longitudinal biomarkers or surrogates for a time to event outcome. This method is an extension of Henderson et al. (2000 Henderson , R. , Diggle , P. , Dobson , A. ( 2000 ). Joint modelling of longitudinal measurements and event time data . Biostatistics 1 ( 4 ): 465 – 480 .[Crossref], [PubMed] , [Google Scholar], 2002 Henderson , R. , Diggle , P. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). In this article, a score test is based on a joint likelihood function which combines the likelihood functions of the longitudinal biomarkers and the survival times. Henderson et al. (2000 Henderson , R. , Diggle , P. , Dobson , A. ( 2000 ). Joint modelling of longitudinal measurements and event time data . Biostatistics 1 ( 4 ): 465 – 480 .[Crossref], [PubMed] , [Google Scholar], 2002 Henderson , R. , Diggle , P. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) assumed that the same random effect exists in the longitudinal component and in the Cox model and then they can derive a score test to determine if a longitudinal biomarker is associated with time to an event. We extend this work and our score test is based on a joint likelihood function which allows other random effects to be present in the survival function.

Considering heterogeneous baseline hazards in individuals, we use simulations to explore how the factors can influence the power of a score test to detect the association of a longitudinal biomarker and the survival time. These factors include the functional form of the random effects from the longitudinal biomarkers, in the different number of individuals, and time points per individual. We illustrate our method using a prothrombin index as a predictor of survival in liver cirrhosis patients.     

Estimators for the Population Mean in the Case of Missing Data

We propose a class of estimators for the population mean when there are missing data in the data set. Obtaining the mean square error equations of the proposed estimators, we show the conditions where the proposed estimators are more efficient than the sample mean, ratio-type estimators, and the estimators in Singh and Horn (2000 Singh , S. , Horn , S. ( 2000 ). Compromised imputation in survey sampling . Metrika 51 : 267 – 276 .[Crossref], [Web of Science ®] , [Google Scholar]) and Singh and Deo (2003 Singh , S. , Deo , B. (2003). Imputation by power transformation. Statist. Pap. 44:555–579.[Crossref], [Web of Science ®] , [Google Scholar]) in the case of missing data. These conditions are also supported by a numerical example.     

A Note on Importance Resampling for Multi-Dimensional Statistics

Johns (1988 Johns , M. V. (1988). Importance sampling for bootstrap confidence intervals. Journal of the American Statistical Association 83:709–714.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Davison (1988 Davison , A. C. ( 1988 ). Discussion of paper by D. V. Hinkley . Journal of the Royal Statistical Society Series B 50 : 356 – 357 . [Google Scholar]), and Do and Hall (1991 Do , K. A. , Hall , P. ( 1991 ). On importance sampling for the bootstrap . Biometrika 78 : 161 – 167 .[Crossref], [Web of Science ®] , [Google Scholar]) used importance sampling for calculating bootstrap distributions of one-dimensional statistics. Realizing that their methods can not be extended easily to multi-dimensional statistics, Fuh and Hu (2004 Fuh , C. D. , Hu , I. ( 2004 ). Efficient importance sampling for events of moderate deviations with applications . Biometrika 91 : 471 – 490 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed an exponential tilting formula for statistics of multi-dimension, which is optimal in the sense that the asymptotic variance is minimized for estimating tail probabilities of asymptotically normal statistics. For one-dimensional statistics, Hu and Su (2008 Hu , J. , Su , Z. ( 2008 ). Adaptive resampling algorithms for estimating bootstrap distributions . Journal of Statistical Planning and Inference 138 ( 6 ): 1763 – 1777 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed a multi-step variance minimization approach that can be viewed as a generalization of the two-step variance minimization approach proposed by Do and Hall (1991 Do , K. A. , Hall , P. ( 1991 ). On importance sampling for the bootstrap . Biometrika 78 : 161 – 167 .[Crossref], [Web of Science ®] , [Google Scholar]). In this article, we generalize the approach of Hu and Su (2008 Hu , J. , Su , Z. ( 2008 ). Adaptive resampling algorithms for estimating bootstrap distributions . Journal of Statistical Planning and Inference 138 ( 6 ): 1763 – 1777 .[Crossref], [Web of Science ®] , [Google Scholar]) to multi-dimensional statistics, which applies to general statistics and does not resort to asymptotics. Empirical results on a real survival data set show that the proposed algorithm provides significant computational efficiency gains.     

Computing the Exact Fisher Information Matrix of Periodic State-Space Models

The purpose of this article is to develop algorithms for computing the exact Fisher information matrix of periodic time-varying state-space models. We first present a relatively simple recursive algorithm which computes the elements of the exact information matrix without involving numerical differentiation, since all required derivatives are analytically evaluated. The proposed algorithm extends the procedure due to Cavanaugh and Shumway (1996 Cavanaugh , J. E. , Shumway , R. H. ( 1996 ). On computing the expected Fisher information matrix for state-space model parameters . Statist. Probab. Lett. 26 : 347 – 355 .[Crossref], [Web of Science ®] , [Google Scholar]) to the periodic state-space framework. Exploiting the approach used in Klein et al. (2000 Klein , A. , Mélard , G. , Zahaf , T. ( 2000 ). Construction of the exact Fisher information matrix of Gaussian time series models by means of matrix differential rules . Linear Alg. Applic. 321 : 209 – 232 .[Crossref], [Web of Science ®] , [Google Scholar]), a second algorithm is proposed in order to obtain the exact information matrix as a whole instead of element by element. The algorithms are first developed in a general framework and then specialized to the case of a periodic Gaussian vector autoregressive moving-average (PVARMA) model.     

An Efficiency and Protection Degree-Based Comparison Among the Quantitative Randomized Response Strategies

There have been many alternative strategies for implementing sampling survey on quantitative characteristic of sensitive issues by using randomized response (RR) technique. The efficiency of most of those strategies has been improved by choosing the suitable design parameters of model. However, the two different procedures with pre-assigned design parameter values cannot ensure that they possess the same protection degree to the respondents. Some earlier comparisons of those strategies are inadequate (as in Eichhorn and Hayre, 1983 Eichhorn , B. H. , Hayre , L. S. ( 1983 ). Scrambled randomized response methods for obtaining sensitive quantitative data . J. Statist. Plann. Infer. 7 : 307 – 316 .[Crossref], [Web of Science ®] , [Google Scholar]; Gupta et al., 2002 Gupta , S. , Gupta , B. , Singh , S. ( 2002 ). Estimation of sensitivity level of personal interview survey questions . J. Statist. Plann. Infer. 100 ( 2 ): 239 – 247 .[Crossref], [Web of Science ®] , [Google Scholar]). Some literature contains a more comprehensive comparison based on efficiency and protection degree to the respondents among the qualitative characteristic RR techniques (see Bhargava and Singh, 2002 Bhargava , M. , Singh , R. ( 2002 ). On the efficiency comparison of certain randomized response strategies . Metrika 55 : 191 – 197 .[Crossref], [Web of Science ®] , [Google Scholar]; Nayak, 1994 Nayak , T. K. ( 1994 ). On randomized response surveys for estimating a proportion . Commun. Statist. Theor. Meth. 23 ( 11 ): 3303 – 3321 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Zaizai and Zankan, 2004 Zaizai , Y. , Zankan , N. ( 2004 ). A fair comparison of the randomized response strategies . Acta Mathematica Scientia 24A ( 3 ): 362 – 368 . [Google Scholar]). As far as the comparisons are concerned that are based on efficiency and protection degree to the respondents among the quantitative characteristic RR techniques, very few related studies have been found so far. The purpose of this article is to give a more adequate comparison among those earlier quantitative characteristic RR strategies. It is found that several important differences between the results obtained in this article and some known results exist. Therefore, these earlier RR strategies should be reevaluated.     

Improved Bar-Lev,Bobovitch, and Boukai Randomized Response Models

In this article, two new improved randomized response models have been proposed. The proposed models are found to be more efficient than the recent randomized response model studied by Bar-Lev et al. (2004 Bar-Lev , S. K. , Bobovitch , E. , Boukai , B. ( 2004 ). A note on randomized response models for quantitative data . Metrika 60 : 255 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]). The relative efficiency of the proposed models has been studied with respect to the Bar-Lev et al. (2004 Bar-Lev , S. K. , Bobovitch , E. , Boukai , B. ( 2004 ). A note on randomized response models for quantitative data . Metrika 60 : 255 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]) model under different situations.     

Bayesian Inference in Dynamic Disequilibrium Models: An Application to the Polish Credit Market

We propose a Bayesian approach for inference in a dynamic disequilibrium model. To circumvent the difficulties raised by the Maddala and Nelson (1974 Maddala , G. , Nelson , F. ( 1974 ). Maximum likelihood methods for models of markets in disequilibrium . Econometrica 42 ( 6 ): 1013 – 1030 .[Crossref], [Web of Science ®] , [Google Scholar]) specification in the dynamic case, we analyze a dynamic extended version of the disequilibrium model of Ginsburgh et al. (1980 Ginsburgh , V. , Tishler , A. , Zang , I. ( 1980 ). Alternative estimation methods for two regime models . European Economic Review 13 : 207 – 228 .[Crossref], [Web of Science ®] , [Google Scholar]). We develop a Gibbs sampler based on the simulation of the missing observations. The feasibility of the approach is illustrated by an empirical analysis of the Polish credit market, for which we conduct a specification search using the posterior deviance criterion of Spiegelhalter et al. (2002 Spiegelhalter , D. J. , Best , N. G. , Carlin , B. P. , Van Der Linde , A. ( 2002 ). Bayesian measures of complexity and fit . Journal of the Royal Statistical Society, Ser. B 64 : 583 – 639 .[Crossref] , [Google Scholar]).     

Empirical Likelihood Ratio for Linear Transformation Models with Doubly Censored Data

Double censoring arises when T represents an outcome variable that can only be accurately measured within a certain range, [L, U], where L and U are the left- and right-censoring variables, respectively. When L is always observed, we consider the empirical likelihood inference for linear transformation models, based on the martingale-type estimating equation proposed by Chen et al. (2002 Chen , K. , Jin , Z. , Ying , Z. ( 2002 ). Semiparametric analysis of transformation models with censored data . Biometrika 89 : 659 – 668 .[Crossref], [Web of Science ®] , [Google Scholar]). It is demonstrated that both the approach of Lu and Liang (2006 Lu , W. , Liang , Y. ( 2006 ). Empirical likelihood inference for linear transformation models . Journal of Multivariate Analysis 97 : 1586 – 1599 .[Crossref], [Web of Science ®] , [Google Scholar]) and that of Yu et al. (2011 Yu , W. , Sun , Y. , Zheng , M. ( 2011 ). Empirical likelihood method for linear transformation models . Annals of the Institute of Statistical Mathematics 63 : 331 – 346 .[Crossref], [Web of Science ®] , [Google Scholar]) can be extended to doubly censored data. Simulation studies are conducted to investigate the performance of the empirical likelihood ratio methods.     

A side sensitive modified group runs control chart to detect shifts in the process mean

Gadre and Rattihalli [5 Gadre, M. P. and Rattihalli, R. N. 2006. Modified group runs control charts to detect increases in fraction non-conforming and shifts in the process mean. Commun. Stat. Simul. Comput., 35: 225–240. [Taylor & Francis Online], [Web of Science ®] [Google Scholar]] have introduced the Modified Group Runs (MGR) control chart to identify the increases in fraction non-conforming and to detect shifts in the process mean. The MGR chart reduces the out-of-control average time-to-signal (ATS), as compared with most of the well-known control charts. In this article, we develop the Side Sensitive Modified Group Runs (SSMGR) chart to detect shifts in the process mean. With the help of numerical examples, it is illustrated that the SSMGR chart performs better than the Shewhart's X¯ chart, the synthetic chart [12 Wu, Z. and Spedding, T. A. 2000. A synthetic control chart for detecting small shifts in the process mean. J. Qual. Technol., 32: 32–38. [Taylor & Francis Online], [Web of Science ®] [Google Scholar]], the Group Runs chart [4 Gadre, M. P. and Rattihalli, R. N. 2004. A group runs control chart for detecting shifts in the process mean. Econ. Qual. Control, 19: 29–43. [Crossref] [Google Scholar]], the Side Sensitive Group Runs chart [6 Gadre, M. P. and Rattihalli, R. N. 2007. A side sensitive group runs control chart for detecting shifts in the process mean. Stat. Methods Appl., 16: 27–37. [Crossref], [Web of Science ®] [Google Scholar]], as well as the MGR chart [5 Gadre, M. P. and Rattihalli, R. N. 2006. Modified group runs control charts to detect increases in fraction non-conforming and shifts in the process mean. Commun. Stat. Simul. Comput., 35: 225–240. [Taylor & Francis Online], [Web of Science ®] [Google Scholar]]. In some situations it is also superior to the Cumulative Sum chart p9 Page, E. S. 1954. Continuous inspection schemes. Biometrika, 41: 100–114. [Crossref], [Web of Science ®] [Google Scholar]] and the exponentially weighed moving average chart [10 Roberts, S. W. 1959. Control chart tests based on geometric moving averages. Technometrics, 1: 239–250. [Taylor & Francis Online] [Google Scholar]]. In the steady state also, its performance is better than the above charts.     

Designs Robust Against the Presence of an Aberration in a Diallel Cross Design Setup

In this article, we find designs insensitive to the presence of an outlier in a diallel cross design setup for estimating a complete set of orthonormal contrasts among the effects of the general combining abilities of a set of parental lines. The criterion of robustness, suggested by Mandal (1989 Mandal , N. K. ( 1989 ). On robust designs . Cal. Stat. Assoc. Bull. 38 : 115 – 119 . [Google Scholar]) in block design setup and used by Biswas (2012 Biswas , A. ( 2012 ). Block designs robust against the presence of an aberration in a treatment-control setup . Commun. Statist. Theor. Meth. 41 : 920 – 933 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in treatment-control setup, is adapted here. Complete diallel cross designs, suggested by Gupta and Kageyama (1994 Gupta , S. , Kageyama , S. ( 1994 ). Optimal complete diallel crosses . Biometrika 81 : 420 – 424 .[Crossref], [Web of Science ®] , [Google Scholar]), and partial diallel cross designs, suggested by Gupta et al. (1995 Gupta , S. , Das , A. , Kageyama , S. ( 1995 ). Single replicate orthogonal block designs for circulant partial diallel crosses . Commun. Statist. A 24 : 2601 – 2607 .[Taylor & Francis Online] , [Google Scholar]) and Mukerjee (1997 Mukerjee , R. ( 1997 ). Optimal partial diallel crosses . Biometrika 84 : 939 – 948 .[Crossref], [Web of Science ®] , [Google Scholar]), are found to be robust under certain conditions.     

Regression M-estimators with One Modified Form of Doubly Censored Data

In this article, we consider the M-estimators for the linear regression model when both response and covariate variables are subject to double censoring. The proposed estimators are constructed as some functional of three types of estimators for a bivariate survival distribution. The first two estimators are the generalizations of the Campbell and Földes (1982 Campbell, G. and Földes, A. 1982. “Large sample properties of nonparametric statistical inference”. In Nonparametric Statistical Inference., Edited by: Gnredenko, B. V., Puri, M. L. and Vineze, I. 103–122. Amsterdam: North-Holland.  [Google Scholar]) and Dabrowska (1988 Dabrowska, D. M. 1988. Kaplan-Meier estimate on the plane. Annals of Statistics, 18: 1475–1489. [Crossref], [Web of Science ®] , [Google Scholar]) estimators proposed by Shen (2009 Shen, P. S. 2009. Nonparametric estimation of the bivariate survival function one modified form of doubly censored data. Computational Statistics, 25: 203–313. [Crossref], [Web of Science ®] , [Google Scholar]). The third estimator is the generalization of the Prentice and Cai (1992 Prentice, R. L. and Cai, J. 1992. Covariance and survivor function estimation using censored multivariate failure time data. Biometrika, 79: 495–512. [Crossref], [Web of Science ®] , [Google Scholar]) estimator. The consistency of the proposed M-estimators is established. A simulation study is conducted to investigate the performance of the proposed estimators. Furthermore, the simple bootstrap methods are used to estimate standard deviations and construct interval estimators.     

An Asymmetric Kernel Estimator of Density Function for Stationary Associated Sequences

Here, we apply the smoothing technique proposed by Chaubey et al. (2007 Chaubey , Y. P. , Sen , A. , Sen , P. K. ( 2007 ). A new smooth density estimator for non-negative random variables. Technical Report No. 1/07. Department of Mathematics and Statistics, Concordia University, Montreal, Canada . [Google Scholar]) for the empirical survival function studied in Bagai and Prakasa Rao (1991 Bagai , I. , Prakasa Rao , B. L. S. ( 1991 ). Estimation of the survival function for stationary associated processes . Statist. Probab. Lett. 12 : 385 – 391 .[Crossref], [Web of Science ®] , [Google Scholar]) for a sequence of stationary non-negative associated random variables.The derivative of this estimator in turn is used to propose a nonparametric density estimator. The asymptotic properties of the resulting estimators are studied and contrasted with some other competing estimators. A simulation study is carried out comparing the recent estimator based on the Poisson weights (Chaubey et al., 2011 Chaubey , Y. P. , Dewan , I. , Li , J. ( 2011 ). Smooth estimation of survival and density functions for a stationary associated process using poisson weights . Statist. Probab. Lett. 81 : 267 – 276 .[Crossref], [Web of Science ®] , [Google Scholar]) showing that the two estimators have comparable finite sample global as well as local behavior.     

A Variance Estimator for Systematic Sampling from a Deliberately Ordered Population

ABSTRACT

The systematic sampling (SYS) design (Madow and Madow, 1944 Madow , L. H. , Madow , W. G. ( 1944 ). On the theory of systematic sampling . Ann. Math. Statist. 15 : 1 – 24 .[Crossref] , [Google Scholar]) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982 Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .[Crossref], [Web of Science ®] , [Google Scholar]). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982 Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .[Crossref], [Web of Science ®] , [Google Scholar]) and usual variance estimators (Yates and Grundy, 1953 Yates , F. , Grundy , P. M. ( 1953 ). Selection without replacement from within strata with probability proportional to size . J. Roy. Statist. Soc. Series B 1 : 253 – 261 . [Google Scholar]) are inadequate and can overestimate the variance significantly (Särndal et al., 1992 Särndal , C. E. , Swenson , B. , Wretman , J. H. ( 1992 ). Model Assisted Survey Sampling . New York : Springer-Verlag , Ch. 3 .[Crossref] , [Google Scholar]). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study.