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.     

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.     

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]).     

Second-Order Covariance Matrix Formula for Heteroskedastic Generalized Linear Models

For the first time, we provide a matrix formula for second-order covariances of maximum likelihood estimates in heteroskedastic generalized linear models, thus generalizing the results of Cordeiro (2004 Cordeiro , G. M. ( 2004 ). Second-order covariance matrix of maximum likelihood estimates in generalized linear models . Statist. Probab. Lett. 66 : 153 – 160 .[Crossref], [Web of Science ®] , [Google Scholar]) and Cordeiro et al. (2006 Cordeiro , G. M. , Barroso , L. P. , Botter , D. A. (2006). Covariance matrix formula for generalized linear models with unknown dispersion. Commun. Statist. Theor. Meth. 35:113–120.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) related to the generalized linear models with known and unknown dispersion parameter, respectively. The covariance matrix formula does not involve cumulants of log-likelihood derivatives and can be easily obtained using simple matrix operations. We apply our main result to a simple model. Some simulations show that the second-order covariances can be quite pronounced in small to moderate samples. The usual covariances of the maximum likelihood estimates can be corrected by these second-order covariances.     

Covariate-Adjusted Partially Linear Regression Models

Motivated by covariate-adjusted regression (CAR) proposed by Sentürk and Müller (2005 Sentürk , D. , Müller , H. G. ( 2005 ). Covariate-adjusted regression . Biometrika 92 : 75 – 89 .[Crossref], [Web of Science ®] , [Google Scholar]) and an application problem, in this article we introduce and investigate a covariate-adjusted partially linear regression model (CAPLM), in which both response and predictor vector can only be observed after being distorted by some multiplicative factors, and an additional variable such as age or period is taken into account. Although our model seems to be a special case of covariate-adjusted varying coefficient model (CAVCM) given by Sentürk (2006 Sentürk , D. ( 2006 ). Covariate-adjusted varying coefficient models . Biostatistics 7 : 235 – 251 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), the data types of CAPLM and CAVCM are basically different and then the methods for inferring the two models are different. In this article, the estimate method motivated by Cui et al. (2008 Cui , X. , Guo , W. S. , Lin , L. , Zhu , L. X. ( 2008 ). Covariate-adjusted nonlinear regression . Ann. Statist. 37 : 1839 – 1870 . [Google Scholar]) is employed to infer the new model. Furthermore, under some mild conditions, the asymptotic normality of estimator for the parametric component is obtained. Combined with the consistent estimate of asymptotic covariance, we obtain confidence intervals for the regression coefficients. Also, some simulations and a real data analysis are made to illustrate the new model and methods.     

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.     

A Benchmarking Approach to Temporal Disaggregation of Economic Time Series by Related Series

Several methods have been devised to deal with the problem of temporal disaggregation of economic time series (a) either when related series are available or (b) when only aggregate figures exist. In this article, we propose a statistical model-based approach to temporal disaggregation of economic time series by related series. The proposed approach is performed in two stages. In the first stage, we evaluate a preliminary estimate of the disaggregated series using a regression model for the disaggregated series and related series observed in the same frequency. The preliminary estimate of disaggregated series obtained in the first step is not consistent with aggregate figures. To ensure consistency we propose in the second stage, the use of a modified benchmarking approach based on signal extraction (Hillmer and Trabelsi, 1987 Hillmer , S. C. , Trabelsi , A. ( 1987 ). Benchmarking of economic time series . J. Amer. Statist. Assoc. 82 ( 400 ): 1064 – 1071 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Trabelsi and Hillmer, 1990 Trabelsi , A. , Hillmer , S. C. ( 1990 ). Benchmarking time series with reliable benchmarks . Appl. Statist. 39 ( 3 ): 367 – 379 .[Crossref], [Web of Science ®] , [Google Scholar]) to adjust the preliminary estimate of disaggregate series. The approach developed here is used for Seasonally Adjusted (SA) and Not Seasonally Adjusted (NSA) data. A comparison with previous temporal disaggregation methods has been done.     

Entropy-Based Moment Selection in the Presence of Weak Identification

Hall et al. (2007 Hall , A. R. , Inoue , A. , Jana , K. , Shin , C. (2007). Information in generalized method of moments estimation and entropy based moment selection. Journal of Econometrics 138:488–512.[Crossref] , [Google Scholar]) propose a method for moment selection based on an information criterion that is a function of the entropy of the limiting distribution of the Generalized Method of Moments (GMM) estimator. They establish the consistency of the method subject to certain conditions that include the identification of the parameter vector by at least one of the moment conditions being considered. In this article, we examine the limiting behavior of this moment selection method when the parameter vector is weakly identified by all the moment conditions being considered. It is shown that the selected moment condition is random and hence not consistent in any meaningful sense. As a result, we propose a two-step procedure for moment selection in which identification is first tested using a statistic proposed by Stock and Yogo (2003 Stock , J. H. , Yogo , M. ( 2003 ). Testing for weak instruments in linear IV regression . Discussion paper, Kennedy School of Government, Harvard University, Cambridge, MA . [Google Scholar]) and then only if this statistic indicates identification does the researcher proceed to the second step in which the aforementioned information criterion is used to select moments. The properties of this two-step procedure are contrasted with those of strategies based on either using all available moments or using the information criterion without the identification pre-test. The performances of these strategies are compared via an evaluation of the finite sample behavior of various methods for inference about the parameter vector. The inference methods considered are based on the Wald statistic, Anderson and Rubin's (1949 Anderson , T. W. , Rubin , H. ( 1949 ). Estimation of the parameters of a single equation in a complete system of stochastic equations . Annals of Mathematical Statistics 20 : 46 – 63 .[Crossref] , [Google Scholar]) statistic, Kleibergen (2002 Kleibergen , F. ( 2002 ). Pivotal statistics for testing structural parameters in instrumenatl variables regression . Econometrica 70 : 1781 – 1803 .[Crossref], [Web of Science ®] , [Google Scholar]) K statistic, and combinations thereof in which the choice is based on the outcome of the test for weak identification.     

A Modified One-Sided Sequential Screening Procedure Based on Individual Misclassification Error

In this article, the modified procedure is proposed by simplifying the procedure of Tsai and Wu (2002 Tsai , H. T. , Wu , S. F. (2002). Sequential screening procedure based on individual misclassification error. IIE Trans. 34:1079–1085.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) by only weighing the screening variables once instead of weighting twice. The numerical comparison of the modified procedure with the old procedure shows that the total inspection cost of the modified procedure is very close to the old one. A theorem is derived to simplify the calculation of all desired probabilities and the expected costs when k-screening variables are allocated into r-stages. Finally, an example of investigating the cycles of failure of silver-zinc batteries is given to illustrate the modified screening procedure.     

The performance of the truncated mixed control chart

Abstract

When the mixed chart proposed by Aslam et al. (2015 Aslam, M., M. Azam, N. Khan, and C.-H. Jun. 2015. A mixed control chart to monitor the process. International Journal of Production Research 53 (15):4684–93. doi:10.1080/00207543.2015.1031354.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is in use, the sample items are classified as defective or not defective and, depending on the number of defectives, the quality characteristic X of the sample items are also measured. In this case, an Xbar chart decides the state of the process. The previous conforming/non-conforming classification truncates the X distribution and, because of that, the mathematical development to obtain the ARLs is complex. Aslam et al. (2015 Aslam, M., M. Azam, N. Khan, and C.-H. Jun. 2015. A mixed control chart to monitor the process. International Journal of Production Research 53 (15):4684–93. doi:10.1080/00207543.2015.1031354.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) didn’t pay attention to the fact that the X distribution is truncated and, due to that, they obtained incorrect ARLs.     

Estimating Incidence Rate on Current Status Data with Application to a Phase IV Cancer Trial

New drug discovery in the pediatrics has dramatically improved survival, but with long- term adverse events. This motivates the examination of adverse outcomes such as long-term toxicity in a phase IV trial. An ideal approach to monitor long-term toxicity is to systematically follow the survivors, which is generally not feasible. Instead, cross-sectional surveys are conducted in Hudson et al. (2007 Hudson , M. M. , Rai , S. N. , Nunez , C. , Merchant , T. E. , Marina , N. M. , Zalamea , N. , Cox , C. , Phipps , S. , Pompeu , R. , Rosenthal , D. ( 2007 ). Noninvasive evaluation of late anthracycline cardiac toxicity in childhood cancer survivors . J. Clin. Oncol. 25 : 3635 – 3643 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), with one of the objectives to estimate the cumulative incidence rates along with specific interest in fixed-term (5 or 10 year) rates. We present inference procedures based on current status data to our motivating example with very interesting findings.     

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.     

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.).     

A Note on Testing Homogeneity of Several Exponential Location Parameters

In this article, the problems of testing homogeneity of several exponential location parameters against simple and tree ordered alternatives are considered separately. Test procedures for both the alternatives are proposed using restricted maximum likelihood estimators (RMLE) of exponential location parameters under the respective orderings. Critical constants for the implementation of the proposed procedures are tabulated. Power comparison of the proposed test procedure under the simple ordered alternative with the procedure of Chen (1982 Chen , H. J. ( 1982 ). A new range statistic for comparisons of several exponential location parameters . Biometrika 69 ( 1 ): 257 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]) and of Dhawan and Gill (1999 Dhawan , A. K. , Gill , A. N. ( 1999 ). A one-sided test for testing homogeneity of scale parameters against ordered alternative . Communication in Statistics—Theory and Methods 28 ( 10 ): 2417 – 2439 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is carried out using Monte-Carlo simulation.     

A Broad Class of Partially Specified Autoregressions on Multi-Casting Data

Extending the bifurcating autoregressive (BAR) process (cf. Cowan and Staudte, 1986 Cowan , R. , Staudte , R. G. ( 1986 ). The bifurcating autoregression model in cell lineage studies . Biometrics 42 : 769 – 783 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) to multi-casting (multi-splitting) data, Hwang and Choi (2009 Hwang , S. Y. , Choi , M. S. ( 2009 ). Modeling and large sample estimation for multi-casting autoregression . Statist. Prob. Lett. 79 : 1943 – 1950 .[Crossref], [Web of Science ®] , [Google Scholar]) introduced multi-casting autoregression (MCAR, for short) defined on multi-casting tree structured data. This article is concerned with the case when the MCAR model is partially specified only through conditional mean and variance without directly imposing autoregressive (AR) structure. The resulting class of models will be referred to as P-MCAR (partially specified MCAR). The P-MCAR considerably enlarges the class of multi-casting models including (as special cases) MCAR, random coefficient MCAR, conditionally heteroscedastic multi-casting models and binomial-thinning processes. Moment structures for this broad P-MCAR class are investigated. Least squares (LS) estimation method is discussed and asymptotic relative efficiency (ARE) of the generalized-LS over ordinary-LS is obtained in a closed form. A simulation study is conducted to illustrate results.     

Nonparametric Estimation Methods of Integrated Multivariate Volatilities

Estimation of integrated multivariate volatilities of an Itô process is an interesting and important issue in finance, for example, in order to evaluate portfolios. New non-parametric estimators have been recently proposed by Malliavin and Mancino (2002 Malliavin , P. , Mancino , M. ( 2002 ). Fourier series method for measurement of multivariate volatilities . Finance and Stochastics 6 : 49 – 61 .[Crossref], [Web of Science ®] , [Google Scholar]) and Hayashi and Yoshida (2005a Hayashi , T. , Yoshida , N. (2005a). On covariance estimation of nonsynchronously observed diffusion processes. Bernoulli 11(2):359–379.[Crossref], [Web of Science ®] , [Google Scholar]) as alternative methods to classical realized quadratic covariation. The purpose of this article is to compare these alternative estimators both theoretically and empirically, when high frequency data is available. We found that the Hayashi–Yoshida estimator performs the best among the alternatives in view of the bias and the MSE. The other estimators are shown to have possibly heavy bias mostly toward the origin. We also applied these estimators to Japanese Government Bond futures to obtain the results consistent with our simulation.     

Improved Predictive Inference for Responses Based on Location Parameter Median from the Rayleigh Model Given a Doubly Censored Sample

The purpose of this article is to investigate the predictive inference for responses from the location parameter mean as well as from the median given a doubly censored sample from the two-parameter Rayleigh model. The predictive results by Khan et al. (2010 Khan , H. M. R. , Provost , S. B. , Ashima , S. ( 2010 ). Predictive Inference from a Two-Parameter Rayleigh Life Model Given a Doubly Censored Sample . Commun. Statist. Theor. Meth. 39 ( 7 ): 1237 – 1246 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) are used to obtain the predictive inference for responses from the median, where Khan et al. (2010 Khan , H. M. R. , Provost , S. B. , Ashima , S. ( 2010 ). Predictive Inference from a Two-Parameter Rayleigh Life Model Given a Doubly Censored Sample . Commun. Statist. Theor. Meth. 39 ( 7 ): 1237 – 1246 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) obtained the future estimates from the mean. A numerical example representing 66 liver cancer patients is used for predictive analysis. It is concluded that the predictive inference from the median gives precise results as compared with the location parameter mean.     

Performance Evaluation of Different Tests for Location Parameters

In this article, our objective is to evaluate the performance of different tests which are used to compare the equality of more than two location parameters. We have considered six tests (including some commonly used) in this study, one of which is parametric and the others are nonparametric. These tests include the usual F test (Fisher and Mackenzie, 1923 Fisher , R. A. , Mackenzie , M. A. ( 1923 ). Studies in crop variation. II. The manurial response of different potato . Journal of Agricultural Science 13 : 311 – 320 .[Crossref], [Web of Science ®] , [Google Scholar]), Kruskal–Wallis test (Kruskall and Wallis, 1952 Kruskall , W. H. , Wallis , W. A. ( 1952 ). Use of ranks in one-criterion variance analysis . Journal of American Statistical Association 47 : 583 – 621 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Kolmogorov–Smirnov test (David, 1958 David , H. T. ( 1958 ). Three-sample Kolnogorov–Smirnov test . The Annals of Mathematical Statistics 29 : 842 – 851 .[Crossref] , [Google Scholar]), the g test (Stekler, 1987 Stekler , H. O. ( 1987 ). Who forecasters better? Journal of Business and Economic Statistics 5 : 155 – 158 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), f test (Batchelor, 1990 Batchelor , R. A. ( 1990 ). All forecasters are equal . Journal of Business and Economic Statistics 8 : 143 – 144 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and Extension of Median test (as given in Daniel, 1990 Daniel , W. W. ( 1990 ). Applied Nonparametric Statistics. , 2nd ed. Duxbury Classic Series , Boston . [Google Scholar]). Performance of these tests are compared under different symmetric, skewed and contaminated probability distributions that include Normal, Cauchy, Uniform, Laplace, Lognormal, Exponential, Weibull, Gamma, t, Chi-square, Half Normal, Mixed Weibull, and Mixed Normal. Performances of these tests are measured in terms of power. We have suggested appropriate tests which may perform better under different situations. It is expected that researchers will find these results useful in decision making.     

Model selection in regression based on pre-smoothing

In this paper, we investigate the effect of pre-smoothing on model selection. Christóbal et al 6 Christóbal Christóbal, J. A., Faraldo Roca, P. and González Manteiga, W. 1987. A class of linear regression parameter estimators constructed by nonparametric estimation. Ann. Statist.,, 15: 603–609. [Crossref], [Web of Science ®] [Google Scholar] showed the beneficial effect of pre-smoothing on estimating the parameters in a linear regression model. Here, in a regression setting, we show that smoothing the response data prior to model selection by Akaike's information criterion can lead to an improved selection procedure. The bootstrap is used to control the magnitude of the random error structure in the smoothed data. The effect of pre-smoothing on model selection is shown in simulations. The method is illustrated in a variety of settings, including the selection of the best fractional polynomial in a generalized linear model.