Comparison of Frailty Models for Acute Leukemia Data under Gompertz Baseline Distribution

In this article, we consider two different shared frailty regression models under the assumption of Gompertz as baseline distribution. Mostly assumption of gamma distribution is considered for frailty distribution. To compare the results with gamma frailty model, we consider the inverse Gaussian shared frailty model also. We compare these two models to a real life bivariate survival data set of acute leukemia remission times (Freireich et al., 1963 Freireich, E.J., Gehan, E., Frei, E., Schroeder, L.R., Wolman, I.J., Anbari, R., Burgert, E.O., Mills, S.D., Pinkel, D., Selawry, O.S., Moon, J.H., Gendel, B.R., Spurr, C.L., Storrs, R., Haurani, F., Hoogstraten, B., Lee, S. (1963). The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukemia: a model for evaluation of other potentially useful therapy. Blood 21:699–716.[Web of Science ®] , [Google Scholar]). Analysis is performed using Markov Chain Monte Carlo methods. Model comparison is made using Bayesian model selection criterion and a well-fitted model is suggested for the acute leukemia data.     

Steady-state Gibbs sampler estimation for lung cancer data

This paper is based on the application of a Bayesian model to a clinical trial study to determine a more effective treatment to lower mortality rates and consequently to increase survival times among patients with lung cancer. In this study, Qian et al. [13 J. Qian, D.K. Stangl, and S. George, A Weibull model for survival data: Using prediction to decide when to stop a clinical trial, in Bayesian Biostatistics, D. Berry and D. Stangl, eds., Marcel Dekker, New York, 1996, pp. 187–205. [Google Scholar]] strived to determine if a Weibull survival model can be used to decide whether to stop a clinical trial. The traditional Gibbs sampler was used to estimate the model parameters. This paper proposes to use the independent steady-state Gibbs sampling (ISSGS) approach, introduced by Dunbar et al. [3 M. Dunbar, H.M. Samawi, R. Vogel, and L. Yu, A more efficient Gibbs sampler estimation using steady state simulation: Application to public health studies, J. Stat. Simul. Comput. 10.1080/00949655.2013.770857.[Taylor &; Francis Online] , [Google Scholar]], to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and improves the performance and convergence of the Gibbs sampler in this application.     

Estimation of finite population mean using two auxiliary variables in stratified two-phase sampling

We propose a new ratio type estimator for estimating the finite population mean using two auxiliary variables in stratified two-phase sampling. Expressions for bias and mean squared error of the proposed estimator are derived up to the first order of approximation. The proposed estimator is more efficient than the usual stratified sample mean estimator, traditional stratified ratio estimator and some other stratified estimators including Bahl and Tuteja (1991 Bahl, S., Tuteja, R. K. (1991). Ratio and product type exponential estimators. Information and Optimization Sciences 12:159–163. [Google Scholar]), Chami et al. (2012 Chami, P. S., Singh, B., Thomas, D. (2012). A two-prameter ratio-product-ratio estimator using auxiliary information. ISRN Probability and Statistics 2012:1–15, doi: 10.5402/2012/103860.[Crossref] , [Google Scholar]), Chand (1975 Chand, L. (1975) Some Ratio Type Estimator Based on two or more Auxiliary Variables, Ph.D. dissertation, Iowa State University, Ames, Iowa (unpublished). [Google Scholar]), Choudhury and Singh (2012 Choudhury, S., Singh, B. K. (2012). A class of chain ratio-product type estimators with two auxiliary variables under double sampling scheme. Journal of the Korean Statistical Society 41:247–256. [Google Scholar]), Hamad et al. (2013 Hamad, N., Hanif, M., Haider, N. (2013). A regression type estimator with two auxiliary variables for two-phase sampling. Open Journal of Statistics, 3:74–78. [Google Scholar]), Vishwakarma and Gangele (2014 Vishwakarma, G. K., Gangele, R. K. (2014). A class of chain ratio-type exponential estimators in double sampling using two auxiliary variates. Applied Mathematics and Computation 227:171–175. [Google Scholar]), Sanaullah et al. (2014 Sanaullah, A., Ali, H. M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Applied Mathematics and Computation 226:541–547. [Google Scholar]), and Chanu and Singh (2014 Chanu, W. K., Singh, B. K. (2014). Improved class of ratio-cum-product estimators of finite population mean in two phase sampling. Global Journal of Science Frontier Research: F Mathematics and Decision Sciences 14(2):1–14. [Google Scholar]).     

Weighting variables in Kohonen competitive learning algorithms

This paper presents a new variable weight method, called the singular value decomposition (SVD) approach, for Kohonen competitive learning (KCL) algorithms based on the concept of Varshavsky et al. [18 R. Varshavsky, A. Gottlieb, M. Linial, and D. Horn, Novel unsupervised feature filtering of bilogical data, Bioinformatics 22 (2006), pp. 507–513.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. Integrating the weighted fuzzy c-means (FCM) algorithm with KCL, in this paper, we propose a weighted fuzzy KCL (WFKCL) algorithm. The goal of the proposed WFKCL algorithm is to reduce the clustering error rate when data contain some noise variables. Compared with the k-means, FCM and KCL with existing variable-weight methods, the proposed WFKCL algorithm with the proposed SVD's weight method provides a better clustering performance based on the error rate criterion. Furthermore, the complexity of the proposed SVD's approach is less than Pal et al. [17 S.K. Pal, R.K. De, and J. Basak, Unsupervised feature evaluation: a neuro-fuzzy approach, IEEE. Trans. Neural Netw. 11 (2000), pp. 366–376.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], Wang et al. [19 X.Z. Wang, Y.D. Wang, and L.J. Wang, Improving fuzzy c-means clustering based on feature-weight learning, Pattern Recognit. Lett. 25 (2004), pp. 1123–1132.[Crossref], [Web of Science ®] , [Google Scholar]] and Hung et al. [9 W. -L. Hung, M. -S. Yang, and D. -H. Chen, Bootstrapping approach to feature-weight selection in fuzzy c-means algorithms with an application in color image segmentation, Pattern Recognit. Lett. 29 (2008), pp. 1317–1325.[Crossref], [Web of Science ®] , [Google Scholar]].     

Adaptive tangent distance classifier on recognition of handwritten digits

Simard et al. [16 Simard, P. Y., LeCun, Y., Denker, J. S. and Victorri, B. 2000. Transformation invariance in pattern recognition: Tangent distance and tangent propagation. J. Imaging Syst. Technol., 11: 181–197.  [Google Scholar] 17 Sona, D., Sperduti, A. and Starita, A. 1997. A constructive learning algorithm for discriminant tangent models. Advances in Neural Information Processing Systems. 1997, Cambridge, MA. Edited by: Mozer, M. C., Jordan, M. I. and Petsche, T. Vol. 9, pp.786–792. MIT Press.  [Google Scholar]] proposed a transformation distance called “tangent distance” (TD) which can make pattern recognition be efficient. The key idea is to construct a distance measure which is invariant with respect to some chosen transformations. In this research, we provide a method using adaptive TD based on an idea inspired by “discriminant adaptive nearest neighbor” [7 Hastie, T., Tibshirani, R. and Friedman, J. 2009. The Elements of Statistical Learning, Data Mining, Inference, and Prediction, 2, New York, Berlin, Heidelberg: Springer. Available at http://www-stat.stanford.edu/ElemStatLearn [Google Scholar]]. This method is relatively easy compared with many other complicated ones. A real handwritten recognition data set is used to illustrate our new method. Our results demonstrate that the proposed method gives lower classification error rates than those by standard implementation of neural networks and support vector machines and is as good as several other complicated approaches.     

Marginal correlation from an extended random-effects model for repeated and overdispersed counts

Vangeneugden et al. [15 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C. and Sotto, C. 2007. Marginal correlation in longitudinal binary data based on generalized linear mixed models, Tech. Rep., Hasselt University. submitted for publication [Google Scholar]] derived approximate correlation functions for longitudinal sequences of general data type, Gaussian and non-Gaussian, based on generalized linear mixed-effects models (GLMM). Their focus was on binary sequences, as well as on a combination of binary and Gaussian sequences. Here, we focus on the specific case of repeated count data, important in two respects. First, we employ the model proposed by Molenberghs et al. [13 Molenberghs, G., Verbeke, G. and Demétrio, C. G.B. 2007. An extended random-effects approach to modeling repeated, overdispersed count data. Lifetime Data Anal., 13: 513–531. [Crossref], [PubMed], [Web of Science ®] [Google Scholar]], which generalizes at the same time the Poisson-normal GLMM and the conventional overdispersion models, in particular the negative-binomial model. The model flexibly accommodates data hierarchies, intra-sequence correlation, and overdispersion. Second, means, variances, and joint probabilities can be expressed in closed form, allowing for exact intra-sequence correlation expressions. Next to the general situation, some important special cases such as exchangeable clustered outcomes are considered, producing insightful expressions. The closed-form expressions are contrasted with the generic approximate expressions of Vangeneugden et al. [15 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C. and Sotto, C. 2007. Marginal correlation in longitudinal binary data based on generalized linear mixed models, Tech. Rep., Hasselt University. submitted for publication [Google Scholar]]. Data from an epileptic-seizures trial are analyzed and correlation functions derived. It is shown that the proposed extension strongly outperforms the classical GLMM.     

A two-stage algorithm for computation of the exact distribution of sums of spacings

Based on the recursions in Huffer (1988 Huffer, F. (1988). Divided differences and the joint distribution of linear combinations of spacings. Journal of Applied Probability 25:346–354. [Google Scholar]) and Huffer and Lin (2001 Huffer, F. W., Lin, C. T. (2001). Computing the joint distribution of general linear combinations of spacings or exponential variates. Statistica Sinica 11:1141–1157. [Google Scholar]), we present a two-stage algorithm and two specialized methods for evaluating the probabilities involving linear combination of spacings of special forms. The two-stage algorithm combines the advantages of marking algorithm in Huffer and Lin (1997 Huffer, F. W., Lin, C. T. (1997). Computing the exact distribution of the extremes of sums of consecutive spacings. Computational Statistics and Data Analysis 26:117–132. [Google Scholar]) and general algorithm in Huffer and Lin (2001 Huffer, F. W., Lin, C. T. (2001). Computing the joint distribution of general linear combinations of spacings or exponential variates. Statistica Sinica 11:1141–1157. [Google Scholar]). The proposed methods can analytically derive the exact expressions for some specific problems, and efficiently handle problems such as the distribution of the circular scan statistic and multiple coverage probabilities.     

EM-based algorithms for autoregressive models with t-distributed innovations

This paper considers the estimation of parameters of AR(p) models for time series with t-distribution via EM-based algorithms. The paper develops asymptotic properties for the estimation to show that the estimators are efficient. Also testing theory for the estimators is considered. The robustness of the estimators and various tests to deviations from an assumed model is investigated. The study shows that the algorithms have equal estimation efficiency even if the error distribution is miss-specified or perturbed by outliers. Interestingly, the estimators from these algorithms performed better than that of the Modified Maximum Likelihood (MML) considered in Tiku et al. (2000 Tiku, M. L., Wong, W. K., Vaughan, D. C., Bian, G. (2000). Time series models in non-normal situations: Symmetric innovations. Journal of Time Series Analysis, 21: 571–596. [Google Scholar]).     

Measures of predictor sensitivity for order-insensitive partitioning of multiple correlation

Lindeman et al. [12 Lindeman, R. H., Merenda, P. F. and Gold, R. Z. 1980. Introduction to Bivariate and Multivariate Analysis, Glenview, IL: Scott Foresman.  [Google Scholar]] provide a unique solution to the relative importance of correlated predictors in multiple regression by averaging squared semi-partial correlations obtained for each predictor across all p! orderings. In this paper, we propose a series of predictor sensitivity statistics that complement the variance decomposition procedure advanced by Lindeman et al. [12 Lindeman, R. H., Merenda, P. F. and Gold, R. Z. 1980. Introduction to Bivariate and Multivariate Analysis, Glenview, IL: Scott Foresman.  [Google Scholar]]. First, we detail the logic of averaging over orderings as a technique of variance partitioning. Second, we assess predictors by conditional dominance analysis, a qualitative procedure designed to overcome defects in the Lindeman et al. [12 Lindeman, R. H., Merenda, P. F. and Gold, R. Z. 1980. Introduction to Bivariate and Multivariate Analysis, Glenview, IL: Scott Foresman.  [Google Scholar]] variance decomposition solution. Third, we introduce a suite of indices to assess the sensitivity of a predictor to model specification, advancing a series of sensitivity-adjusted contribution statistics that allow for more definite quantification of predictor relevance. Fourth, we describe the analytic efficiency of our proposed technique against the Budescu conditional dominance solution to the uneven contribution of predictors across all p! orderings.     

Asymptotic Results for a Generalized Pólya Urn with “Multi-Updating” and Applications to Clinical Trials

In this article, a new Pólya urn model is introduced and studied; in particular, a strong law of large numbers and two central limit theorems are proved. This urn generalizes a model studied in Berti et al. (2004 Berti , P. , Pratelli , L. , Rigo , P. ( 2004 ). Limit theorems for a class of identically distributed random variables . Ann. Probab. 32 ( 3A ): 2029 – 2052 . [Google Scholar]), May et al. (2005 May , C. , Paganoni , A. M. , Secchi , P. ( 2005 ). On a two-color generalized Pólya urn . Metron 63 ( 1 ): 115 – 134 . [Google Scholar]), and in Crimaldi (2007 Crimaldi , I. ( 2007 ). Almost sure conditional convergence for a generalized Pólya urn. Submitted. Available at: http://amsacta.cib.unibo.it/archive/00002468  [Google Scholar]), and it has natural applications in clinical trials. Indeed, the model includes both delayed and missing (or null) responses. Moreover, a connection with the conditional identity in distribution of Berti et al. (2004 Berti , P. , Pratelli , L. , Rigo , P. ( 2004 ). Limit theorems for a class of identically distributed random variables . Ann. Probab. 32 ( 3A ): 2029 – 2052 . [Google Scholar]) is given.     

Refined Inference on Long Memory in Realized Volatility

There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et al., 2001 Andersen , T. G. , Bollerslev , T. , Diebold , F. X. , Labys , P. ( 2001 ). The distribution of realized exchange rate volatility . Journal of the American Statistical Association 96 ( 453 ): 42 – 55 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Martens et al., 2004 Martnes , M. , Van Dijk , D. , De Pooter , M. ( 2004 ). Modeling and forecasting S&P 500 volatility: Long memory, structural breaks and nonlinearity. Tinbergen Institute Discussion Paper 2004-067/4 . [Google Scholar]). The present article provides some illustrative analysis of how long memory may arise from the accumulative process underlying realized volatility. The article also uses results in Lieberman and Phillips (2004 Lieberman , O. , Phillips , P. C. B. ( 2004 ). Expansions for the distribution of the maximum likelihood estimator of the fractional difference parameter . Econometric Theory 20 ( 3 ): 464 – 484 . [Google Scholar], 2005 Lieberman , O. , Phillips , P. C. B. ( 2005 ). Expansions for approximate maximum likelihood estimators of the fractional difference parameter . The Econometrics Journal 8 : 367 – 379 . [Google Scholar]) to refine statistical inference about d by higher order theory. Standard asymptotic theory has an O(n ^?1/2) error rate for error rejection probabilities, and the theory used here refines the approximation to an error rate of o(n ^?1/2). The new formula is independent of unknown parameters, is simple to calculate and user-friendly. The method is applied to test whether the reported long memory parameter estimates of Andersen et al. (2001 Andersen , T. G. , Bollerslev , T. , Diebold , F. X. , Labys , P. ( 2001 ). The distribution of realized exchange rate volatility . Journal of the American Statistical Association 96 ( 453 ): 42 – 55 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Martens et al. (2004 Martnes , M. , Van Dijk , D. , De Pooter , M. ( 2004 ). Modeling and forecasting S&P 500 volatility: Long memory, structural breaks and nonlinearity. Tinbergen Institute Discussion Paper 2004-067/4 . [Google Scholar]) differ significantly from the lower boundary (d = 0.5) of nonstationary long memory, and generally confirms earlier findings.     

A new estimator of finite population mean based on the dual use of the auxiliary information

When a sufficient correlation between the study variable and the auxiliary variable exists, the ranks of the auxiliary variable are also correlated with the study variable, and thus, these ranks can be used as an effective tool in increasing the precision of an estimator. In this paper, we propose a new improved estimator of the finite population mean that incorporates the supplementary information in forms of: (i) the auxiliary variable and (ii) ranks of the auxiliary variable. Mathematical expressions for the bias and the mean-squared error of the proposed estimator are derived under the first order of approximation. The theoretical and empirical studies reveal that the proposed estimator always performs better than the usual mean, ratio, product, exponential-ratio and -product, classical regression estimators, and Rao (1991 Rao, T.J. (1991). On certail methods of improving ration and regression estimators. Commun. Stat. Theory Methods 20(10):3325–3340.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), Singh et al. (2009 Singh, R., Chauhan, P., Sawan, N., Smarandache, F. (2009). Improvement in estimating the population mean using exponential estimator in simple random sampling. Int. J. Stat. Econ. 3(A09):13–18. [Google Scholar]), Shabbir and Gupta (2010 Shabbir, J., Gupta, S. (2010). On estimating finite population mean in simple and stratified random sampling. Commun. Stat. Theory Methods 40(2):199–212.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), Grover and Kaur (2011 Grover, L.K., Kaur, P. (2011). An improved estimator of the finite population mean in simple random sampling. Model Assisted Stat. Appl. 6(1):47–55. [Google Scholar], 2014) estimators.     

Marginal Correlation from Logit- and Probit-Beta-Normal Models for Hierarchical Binary Data

In hierarchical data settings, be it of a longitudinal, spatial, multi-level, clustered, or otherwise repeated nature, often the association between repeated measurements attracts at least part of the scientific interest. Quantifying the association frequently takes the form of a correlation function, including but not limited to intraclass correlation. Vangeneugden et al. (2010 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C., Sotto, C. (2010). Marginal correlation in longitudinal binary data based on generalized linear mixed models. Communi. Stati. Theory &; Methods. 39:3542–3557. [Google Scholar]) derived approximate correlation functions for longitudinal sequences of general data type, Gaussian and non-Gaussian, based on generalized linear mixed-effects models. Here, we consider the extended model family proposed by Molenberghs et al. (2010 Molenberghs, G., Verbeke, G., Demétrio, C., Vieira, A. (2010). A family of generalized linear models for repeated measures with normal and conjugate random effects. Stat. Sci. 25:325–347.[Crossref], [Web of Science ®] , [Google Scholar]). This family flexibly accommodates data hierarchies, intra-sequence correlation, and overdispersion. The family allows for closed-form means, variance functions, and correlation function, for a variety of outcome types and link functions. Unfortunately, for binary data with logit link, closed forms cannot be obtained. This is in contrast with the probit link, for which such closed forms can be derived. It is therefore that we concentrate on the probit case. It is of interest, not only in its own right, but also as an instrument to approximate the logit case, thanks to the well-known probit-logit ‘conversion.’ Next to the general situation, some important special cases such as exchangeable clustered outcomes receive attention because they produce insightful expressions. The closed-form expressions are contrasted with the generic approximate expressions of Vangeneugden et al. (2010 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C., Sotto, C. (2010). Marginal correlation in longitudinal binary data based on generalized linear mixed models. Communi. Stati. Theory &; Methods. 39:3542–3557. [Google Scholar]) and with approximations derived for the so-called logistic-beta-normal combined model. A simulation study explores performance of the method proposed. Data from a schizophrenia trial are analyzed and correlation functions derived.     

A link-free sparse group variable selection method for single-index model

For regression problems with grouped covariates, we adapt the idea of sparse group lasso (SGL) [10 J. Friedman, T. Hastie, and R. Tibshirani, A note on the group lasso and a sparse group lasso, Tech. Rep., Statistics Department, Stanford University, 2010. [Google Scholar]] to the framework of the sufficient dimension reduction. Assuming that the regression falls into a single-index structure, we propose a method called the sparse group sufficient dimension reduction to conduct group and within-group variable selections simultaneously without assuming a specific link function. Simulation studies show that our method is comparable to the SGL under the regular linear model setting and outperforms SGL with higher true positive rates and substantially lower false positive rates when the regression function is nonlinear. One immediate application of our method is to the gene pathway data analysis where genes naturally fall into groups (pathways). An analysis of a glioblastoma microarray data is included for illustration of our method.     

A Bayesian approach to analyse overdispersed longitudinal count data

In this paper, we consider a model for repeated count data, with within-subject correlation and/or overdispersion. It extends both the generalized linear mixed model and the negative-binomial model. This model, proposed in a likelihood context [17 G. Molenberghs, G. Verbeke, and C.G.B. Demétrio, An extended random-effects approach to modeling repeated, overdispersion count data, Lifetime Data Anal. 13 (2007), pp. 457–511.[Web of Science ®] , [Google Scholar],18 G. Molenberghs, G. Verbeke, C.G.B. Demétrio, and A. Vieira, A family of generalized linear models for repeated measures with normal and conjugate random effects, Statist. Sci. 25 (2010), pp. 325–347. doi: 10.1214/10-STS328[Crossref], [Web of Science ®] , [Google Scholar]] is placed in a Bayesian inferential framework. An important contribution takes the form of Bayesian model assessment based on pivotal quantities, rather than the often less adequate DIC. By means of a real biological data set, we also discuss some Bayesian model selection aspects, using a pivotal quantity proposed by Johnson [12 V.E. Johnson, Bayesian model assessment using pivotal quantities, Bayesian Anal. 2 (2007), pp. 719–734. doi: 10.1214/07-BA229[Crossref], [Web of Science ®] , [Google Scholar]].     

An intuitive clustering algorithm for spherical data with application to extrasolar planets

This paper proposes an intuitive clustering algorithm capable of automatically self-organizing data groups based on the original data structure. Comparisons between the propopsed algorithm and EM [1 A. Banerjee, I.S. Dhillon, J. Ghosh, and S. Sra, Clustering on the unit hypersphere using von Mises–Fisher distribution, J. Mach. Learn. Res. 6 (2005), pp. 1–39. [Google Scholar]] and spherical k-means [7 I.S. Dhillon and D.S. Modha, Concept decompositions for large sparse text data using clustering, Mach. Learn. 42 (2001), pp. 143–175. doi: 10.1023/A:1007612920971[Crossref], [Web of Science ®] , [Google Scholar]] algorithms are given. These numerical results show the effectiveness of the proposed algorithm, using the correct classification rate and the adjusted Rand index as evaluation criteria [5 J.-M. Chiou and P.-L. Li, Functional clustering and identifying substructures of longitudinal data, J. R. Statist. Soc. Ser. B. 69 (2007), pp. 679–699. doi: 10.1111/j.1467-9868.2007.00605.x[Crossref] , [Google Scholar],6 J.-M. Chiou and P.-L. Li, Correlation-based functional clustering via subspace projection, J. Am. Statist. Assoc. 103 (2008), pp. 1684–1692. doi: 10.1198/016214508000000814[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. In 1995, Mayor and Queloz announced the detection of the first extrasolar planet (exoplanet) around a Sun-like star. Since then, observational efforts of astronomers have led to the detection of more than 1000 exoplanets. These discoveries may provide important information for understanding the formation and evolution of planetary systems. The proposed clustering algorithm is therefore used to study the data gathered on exoplanets. Two main implications are also suggested: (1) there are three major clusters, which correspond to the exoplanets in the regimes of disc, ongoing tidal and tidal interactions, respectively, and (2) the stellar metallicity does not play a key role in exoplanet migration.     

Searching effective rotation patterns for population median using exponential type estimators in two-occasion rotation sampling

ABSTRACT

The present article is an attempt to explore the rotation patterns using exponential ratio type estimators for the estimation of finite population median at current occasion in two occasion rotation sampling. Properties of the proposed estimators including the optimum replacement strategies have been elaborated. The proposed estimators have been compared with sample median estimator when there is no matching from previous occasion as well with the ratio type estimator proposed by Singh et al. (2007 Singh, H.P., Tailor, R., Singh, S., Kim, Jong-Min. (2007). Quintile estimation in successive sampling. J. Kor. Stat. Soc. 36(4):543–556. [Google Scholar]) for second quantile. The behaviors of the proposed estimators are justified by empirical interpretations and validated by means of simulation study with the help of some natural populations.     

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.     

On evaluating the performance of different forecasters

In this article, we have evaluated the performance of different forecasters and tested association between their performances for different pairs of variables. We have used three data sets of track records of professional U.S. economic forecasters participating in the Blue Chip consensus forecasting service (the data sets contain the root mean square errors (RMSE) of different forecasters for different years). To evaluate the performance of forecasters we have covered three well-known tests, namely the usual F test (cf. Fisher (1923 Fisher, R. A., Mackenzie, M. A. (1923). Studied in crop variation II. The manurial response of different potato. Journal of Agricultural Science 13:311–320. [Google Scholar])), Kruskal Wallis test (cf. Kruskal 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. [Google Scholar])), and Extension of Median test (cf. Daniel (1990 Daniel, W. W. (1990). Applied Nonparametric Statistics. Duxbury Classic Series. (2nd Ed.), Boston. [Google Scholar])). To test the association between the forecaster's performances for different pairs of variables, we have considered Gini mean correlation coefficient r_g1 (cf. Yitzhaki, S., and Olkin, I. (1991 Yitzhaki, S., Olkin, I. (1991). Concentration indices and concentration curves, in K. Mosler and M. Scarsini (eds.), Stochastic Orders and Decisions under Risk, Institute of Mathematical Statistics: Lecture-Notes Monograph Series, 19, 1991, 380–392. [Google Scholar]) and Yitzhaki (2003 Yitzaki, S. (2003). Gini mean difference: A superior measure of variability for non normal distribution. Metron-International Journal of Statistics, LXI:285–316. [Google Scholar])), Modified rank correlation coefficient (cf. Zimmerman (1994 Zimmerman, D. W. (1994). A Note on modified rank correlation. Journal of educational and Behavioral Statistics 19:357–362. [Google Scholar])) and three modifications of Spearman rank correlation coefficient. We have observed that different forecasters do not necessarily offer same average performance. Moreover, an evidence of association between two criteria does not always lead us reaching at the same decision. The outcomes of the study may help the practitioners in selecting the best forecaster(s) for policymaking purposes.     

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.