Nonparametric Comparison for Multivariate Panel Count Data

Multivariate panel count data often occur when there exist several related recurrent events or response variables defined by occurrences of related events. For univariate panel count data, several nonparametric treatment comparison procedures have been developed. However, it does not seem to exist a nonparametric procedure for multivariate cases. Based on differences between estimated mean functions, this article proposes a class of nonparametric test procedures for multivariate panel count data. The asymptotic distribution of the new test statistics is established and a simulation study is conducted. Moreover, the new procedures are applied to a skin cancer problem that motivated this study.     

Bayes Factor Consistency for One-way Random Effects Model

In this article, we consider Bayesian hypothesis testing for the balanced one-way random effects model. A special choice of the prior formulation for the ratio of variance components is shown to yield an explicit closed-form Bayes factor without integral representation. Furthermore, we study the consistency issue of the resulting Bayes factor under three asymptotic scenarios: either the number of units goes to infinity, the number of observations per unit goes to infinity, or both go to infinity. Finally, the behavior of the proposed approach is illustrated by simulation studies.     

一类基于非参数回归的条件异方差检验

现有基于参数模型构造的条件异方差检验往往存在模型设定偏误问题。为了避免模型误设对检验结果的影响,并且同时捕获多种条件异方差现象,本文基于非参数回归构造了不依赖于特定模型形式的条件异方差检验统计量。该统计量可视作条件方差和无条件方差之间差异的加权平均,在原假设成立时渐近服从标准正态分布。数值模拟结果一方面表明本文统计量具有良好的有限样本性质,另一方面也说明条件均值模型误设会导致错误地拒绝条件同方差的原假设,凸显了本文引入非参数方法构造条件异方差检验的必要性。实证分析采用本文统计量探讨了国际主要股指收益率的条件异方差现象,得到了与Engle (1982)不同的检验结果,可能意味着股指收益率呈现出非线性动态特征。     

Restricted most powerful Bayesian tests for linear models

Uniformly most powerful Bayesian tests (UMPBTs) are a new class of Bayesian tests in which null hypotheses are rejected if their Bayes factor exceeds a specified threshold. The alternative hypotheses in UMPBTs are defined to maximize the probability that the null hypothesis is rejected. Here, we generalize the notion of UMPBTs by restricting the class of alternative hypotheses over which this maximization is performed, resulting in restricted most powerful Bayesian tests (RMPBTs). We then derive RMPBTs for linear models by restricting alternative hypotheses to g priors. For linear models, the rejection regions of RMPBTs coincide with those of usual frequentist F‐tests, provided that the evidence thresholds for the RMPBTs are appropriately matched to the size of the classical tests. This correspondence supplies default Bayes factors for many common tests of linear hypotheses. We illustrate the use of RMPBTs for ANOVA tests and t‐tests and compare their performance in numerical studies.     

江苏省乡镇卫生院住院费用影响因素的抽样分析

目的：分析我省部分乡镇卫生院住院患者的住院费用特点及其影响因素,为合理优化乡镇卫生院收费管理,解决农民＂看病难、看病贵＂问题提供基线资料。方法：采用整群抽样方法,调查省内4家乡镇卫生院住院患者的相关资料,用SPSS 13.0软件对住院费用进行统计描述、住院天数与住院费用的曲线估计、住院费用影响因素的方差分析、秩和检验等。结果：西药费用占患者住院费用比例最高;住院天数与住院费用呈直线相关;患者的年龄与治疗效果对住院费用有显著影响,性别和住院科别对住院费用的影响无统计学意义。结论：应从提高乡镇医院医疗质量,缩短住院天数,合理控制药品费用,建立健全医疗保障体系几方面着手,减少住院费用。     

Nonparametric depth-based multivariate outlier identifiers, and masking robustness properties

In extending univariate outlier detection methods to higher dimension, various issues arise: limited visualization methods, inadequacy of marginal methods, lack of a natural order, limited parametric modeling, and, when using Mahalanobis distance, restriction to ellipsoidal contours. To address and overcome such limitations, we introduce nonparametric multivariate outlier identifiers based on multivariate depth functions, which can generate contours following the shape of the data set. Also, we study masking robustness, that is, robustness against misidentification of outliers as nonoutliers. In particular, we define a masking breakdown point (MBP), adapting to our setting certain ideas of Davies and Gather [1993. The identification of multiple outliers (with discussion). Journal of the American Statistical Association 88, 782–801] and Becker and Gather [1999. The masking breakdown point of multivariate outlier identification rules. Journal of the American Statistical Association 94, 947–955] based on the Mahalanobis distance outlyingness. We then compare four affine invariant outlier detection procedures, based on Mahalanobis distance, halfspace or Tukey depth, projection depth, and “Mahalanobis spatial” depth. For the goal of threshold type outlier detection, it is found that the Mahalanobis distance and projection procedures are distinctly superior in performance, each with very high MBP, while the halfspace approach is quite inferior. When a moderate MBP suffices, the Mahalanobis spatial procedure is competitive in view of its contours not constrained to be elliptical and its computational burden relatively mild. A small sampling experiment yields findings completely in accordance with the theoretical comparisons. While these four depth procedures are relatively comparable for the purpose of robust affine equivariant location estimation, the halfspace depth is not competitive with the others for the quite different goal of robust setting of an outlyingness threshold.     

Robust estimation and testing in one-way ANOVA for Type II censored samples: skew normal error terms

Censoring can be occurred in many statistical analyses in the framework of experimental design. In this study, we estimate the model parameters in one-way ANOVA under Type II censoring. We assume that the distribution of the error terms is Azzalini's skew normal. We use Tiku's modified maximum likelihood (MML) methodology which is a modified version of the well-known maximum likelihood (ML) in the estimation procedure. Unlike ML methodology, MML methodology is non-iterative and gives explicit estimators of the model parameters. We also propose new test statistics based on the proposed estimators. The performances of the proposed estimators and the test statistics based on them are compared with the corresponding normal theory results via Monte Carlo simulation study. A real life data is analysed to show the implementation of the methodology presented in this paper at the end of the study.     

Release velocities and bowler performance in cricket

There is a widespread notion in the cricketing world that with increasing pace the performance of a bowler improves. Additionally, many cricket experts believe faster bowlers to be more effective against lower order batters than bowlers who bowl at slower speeds. The present study puts these two ubiquitous notions under test by statistically analysing the differences in performance of bowlers from three subpopulations based on average release velocities. Results from one-way ANOVA (and its modified versions), for international test matches, reveal faster bowlers to be performing better, in terms of Average and Strike-rate, but no significant differences in the Economy rate and Dynamic Bowling rate. Faster bowlers were found to be more effective in taking wickets of lower and middle order batters as compared to bowlers with less pace. However, there was no statistically significant difference in performance of Fast and Fast-Medium bowlers against a top-order batter.     

An evaluation of the bootstrap for model validation in mixture models

Bootstrapping has been used as a diagnostic tool for validating model results for a wide array of statistical models. Here we evaluate the use of the non-parametric bootstrap for model validation in mixture models. We show that the bootstrap is problematic for validating the results of class enumeration and demonstrating the stability of parameter estimates in both finite mixture and regression mixture models. In only 44% of simulations did bootstrapping detect the correct number of classes in at least 90% of the bootstrap samples for a finite mixture model without any model violations. For regression mixture models and cases with violated model assumptions, the performance was even worse. Consequently, we cannot recommend the non-parametric bootstrap for validating mixture models.

The cause of the problem is that when resampling is used influential individual observations have a high likelihood of being sampled many times. The presence of multiple replications of even moderately extreme observations is shown to lead to additional latent classes being extracted. To verify that these replications cause the problems we show that leave-k-out cross-validation where sub-samples taken without replacement does not suffer from the same problem.