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Journal of Statistical Planning and Inference

J McGinniss, O Harel
Missing values present challenges in the analysis of data across many areas of research. Handling incomplete data incorrectly can lead to bias, over-confident intervals, and inaccurate inferences. One principled method of handling incomplete data is multiple imputation. This article considers incomplete data in which values are missing for three or more qualitatively different reasons and applies a modified multiple imputation framework in the analysis of that data. Included are a proof of the methodology used for three-stage multiple imputation with its limiting distribution, an extension to more than three types of missing values, an extension to the ignorability assumption with proof, and simulations demonstrating that the estimator is unbiased and efficient under the ignorability assumption...
September 2016: Journal of Statistical Planning and Inference
Jun Dong, Jason P Estes, Gang Li, Damla Şentürk
Varying coefficient models are useful for modeling longitudinal data and have been extensively studied in the past decade. Motivated by commonly encountered dichotomous outcomes in medical and health cohort studies, we propose a two-step method to estimate the regression coefficient functions in a logistic varying coefficient model for a longitudinal binary outcome. The model depicts time-varying covariate effects without imposing stringent parametric assumptions. The proposed estimation is simple and can be conveniently implemented using existing statistical packages such as SAS and R...
July 2016: Journal of Statistical Planning and Inference
Michail Papathomas, Sylvia Richardson
This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist log-linear model determination, demonstrating advantages and limitations with simulated and real data sets...
June 2016: Journal of Statistical Planning and Inference
Limin Peng, Amita Manatunga, Ming Wang, Ying Guo, Akm Fazlur Rahman
In practice, disease outcomes are often measured in a continuous scale, and classification of subjects into meaningful disease categories is of substantive interest. To address this problem, we propose a general analytic framework for determining cut-points of the continuous scale. We develop a unified approach to assessing optimal cut-points based on various criteria, including common agreement and association measures. We study the nonparametric estimation of optimal cut-points. Our investigation reveals that the proposed estimator, though it has been ad-hocly used in practice, pertains to nonstandard asymptotic theory and warrants modifications to traditional inferential procedures...
May 1, 2016: Journal of Statistical Planning and Inference
Jeankyung Kim, Hyune-Ju Kim
The Schwarz criterion or Bayes Information Criterion (BIC) is often used to select a model dimension, and some variations of the BIC have been proposed in the context of change-point problems. In this paper, we consider a segmented line regression model with an unknown number of change-points and study asymptotic properties of Schwarz type criteria in selecting the number of change-points. Noticing the overestimating tendency of the traditional BIC observed in some empirical studies and being motivated by asymptotic behavior of the modified BIC proposed by Zhang and Siegmund (2007), we consider a variation of the Schwarz type criterion that applies a harsher penalty equivalent to the model with one additional unknown parameter per segment...
March 1, 2016: Journal of Statistical Planning and Inference
Andrew Waters, Kassandra Fronczyk, Michele Guindani, Richard G Baraniuk, Marina Vannucci
We develop a modeling framework for joint factor and cluster analysis of datasets where multiple categorical response items are collected on a heterogeneous population of individuals. We introduce a latent factor multinomial probit model and employ prior constructions that allow inference on the number of factors as well as clustering of the subjects into homogenous groups according to their relevant factors. Clustering, in particular, allows us to borrow strength across subjects, therefore helping in the estimation of the model parameters, particularly when the number of observations is small...
November 2015: Journal of Statistical Planning and Inference
Zhengjia Chen, Xinjia Chen
In this article, we propose rigorous sample size methods for estimating the means of random variables, which require no information of the underlying distributions except that the random variables are known to be bounded in a certain interval. Our sample size methods can be applied without assuming that the samples are identical and independent. Moreover, our sample size methods involve no approximation. We demonstrate that the sample complexity can be significantly reduced by using a mixed error criterion...
February 2015: Journal of Statistical Planning and Inference
Abel Rodríguez, Fernando A Quintana
We discuss fully Bayesian inference in a class of species sampling models that are induced by residual allocation (sometimes called stick-breaking) priors on almost surely discrete random measures. This class provides a generalization of the well-known Ewens sampling formula that allows for additional flexibility while retaining computational tractability. In particular, the procedure is used to derive the exchangeable predictive probability functions associated with the generalized Dirichlet process of Hjort (2000) and the probit stick-breaking prior of Chung and Dunson (2009) and Rodriguez and Dunson (2011)...
February 2015: Journal of Statistical Planning and Inference
Ana-Maria Staicu, Soumen N Lahiri, Raymond J Carroll
We propose an L (2)-norm based global testing procedure for the null hypothesis that multiple group mean functions are equal, for functional data with complex dependence structure. Specifically, we consider the setting of functional data with a multilevel structure of the form groups-clusters or subjects-units, where the unit-level profiles are spatially correlated within the cluster, and the cluster-level data are independent. Orthogonal series expansions are used to approximate the group mean functions and the test statistic is estimated using the basis coefficients...
January 2015: Journal of Statistical Planning and Inference
Michael Rosenblum
We take the perspective of a researcher planning a randomized trial of a new treatment, where it is suspected that certain subpopulations may benefit more than others. These subpopulations could be defined by a risk factor or biomarker measured at baseline. We focus on situations where the overall population is partitioned into two, predefined subpopulations. When the true average treatment effect for the overall population is positive, it logically follows that it must be positive for at least one subpopulation...
December 2014: Journal of Statistical Planning and Inference
Jay Bartroff, Jinlin Song
This paper addresses the following general scenario: A scientist wishes to perform a battery of experiments, each generating a sequential stream of data, to investigate some phenomenon. The scientist would like to control the overall error rate in order to draw statistically-valid conclusions from each experiment, while being as efficient as possible. The between-stream data may differ in distribution and dimension but also may be highly correlated, even duplicated exactly in some cases. Treating each experiment as a hypothesis test and adopting the familywise error rate (FWER) metric, we give a procedure that sequentially tests each hypothesis while controlling both the type I and II FWERs regardless of the between-stream correlation, and only requires arbitrary sequential test statistics that control the error rates for a given stream in isolation...
October 1, 2014: Journal of Statistical Planning and Inference
Yao Yu, Sally W Thurston, Russ Hauser, Hua Liang
This paper is concerned with model selection and model averaging procedures for partially linear single-index models. The profile least squares procedure is employed to estimate regression coefficients for the full model and submodels. We show that the estimators for submodels are asymptotically normal. Based on the asymptotic distribution of the estimators, we derive the focused information criterion (FIC), formulate the frequentist model average (FMA) estimators and construct proper confidence intervals for FMA estimators and FIC estimator, a special case of FMA estimators...
December 1, 2013: Journal of Statistical Planning and Inference
Molin Wang, Xiaomei Liao, Donna Spiegelman
This paper considers 2×2 tables arising from case-control studies in which the binary exposure may be misclassified. We found circumstances under which the inverse matrix method provides a more efficient odds ratio estimator than the naive estimator. We provide some intuition for the findings, and also provide a formula for obtaining the minimum size of a validation study such that the variance of the odds ratio estimator from the inverse matrix method is smaller than that of the naive estimator, thereby ensuring an advantage for the misclassification corrected result...
November 1, 2013: Journal of Statistical Planning and Inference
Kurt Hornik, Bettina Grün
This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises-Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises-Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrix-valued) von Mises-Fisher distributions on Stiefel manifolds...
May 2013: Journal of Statistical Planning and Inference
Inyoung Kim, Herbert Pang, Hongyu Zhao
Most statistical methods for microarray data analysis consider one gene at a time, and they may miss subtle changes at the single gene level. This limitation may be overcome by considering a set of genes simultaneously where the gene sets are derived from prior biological knowledge. We call a pathway as a predefined set of genes that serve a particular cellular or physiological function. Limited work has been done in the regression settings to study the effects of clinical covariates and expression levels of genes in a pathway on a continuous clinical outcome...
April 2013: Journal of Statistical Planning and Inference
Chih-Chi Hu, Ying Kuen Cheung
Dose-finding in clinical studies is typically formulated as a quantile estimation problem, for which a correct specification of the variance function of the outcomes is important. This is especially true for sequential study where the variance assumption directly involves in the generation of the design points and hence sensitivity analysis may not be performed after the data are collected. In this light, there is a strong reason for avoiding parametric assumptions on the variance function, although this may incur efficiency loss...
March 2013: Journal of Statistical Planning and Inference
Albert Vexler, Wei Deng, Gregory E Wilding
Bayes methodology provides posterior distribution functions based on parametric likelihoods adjusted for prior distributions. A distribution-free alternative to the parametric likelihood is use of empirical likelihood (EL) techniques, well known in the context of nonparametric testing of statistical hypotheses. Empirical likelihoods have been shown to exhibit many of the properties of conventional parametric likelihoods. In this article, we propose and examine Bayes factors (BF) methods that are derived via the EL ratio approach...
March 1, 2013: Journal of Statistical Planning and Inference
Hong Zhang, Donglin Zeng, Sylviane Olschwang, Kai Yu
A formal semiparametric statistical inference framework is proposed for the evaluation of the age-dependent penetrance of a rare genetic mutation, using family data generated under a case-family design, where phenotype and genotype information are collected from first-degree relatives of case probands carrying the targeted mutation. The proposed approach allows for unobserved risk factors that are correlated among family members. Some rigorous large sample properties are established, which show that the proposed estimators were asymptotically semi-parametric efficient...
February 2013: Journal of Statistical Planning and Inference
Albert Vexler, Gregory Gurevich, Alan D Hutson
The Wilcoxon rank-sum test and its variants are historically well-known to be very powerful nonparametric decision rules for testing no location difference between two groups given paired data versus a shift alternative. In this article, we propose a new alternative empirical likelihood (EL) ratio approach for testing the equality of marginal distributions given that sampling is from a continuous bivariate population. We show that in various shift alternative scenarios the proposed exact test is superior to the classic nonparametric procedures, which may break down completely or are frequently inferior to the density-based EL ratio test...
February 1, 2013: Journal of Statistical Planning and Inference
Yi Cheng, Yu Shen
We propose an efficient group sequential monitoring rule for clinical trials. At each interim analysis both efficacy and futility are evaluated through a specified loss structure together with the predicted power. The proposed design is robust to a wide range of priors, and achieves the specified power with a saving of sample size compared to existing adaptive designs. A method is also proposed to obtain a reduced-bias estimator of treatment difference for the proposed design. The new approaches hold great potential for efficiently selecting a more effective treatment in comparative trials...
February 1, 2013: Journal of Statistical Planning and Inference
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