Estimation of noncentrality parameters

We propose some estimators of noncentrality parameters which improve upon usual unbiased estimators under quadratic loss. The distributions we consider are the noncentral chi-square and the noncentral F. However, we give more general results for the family of elliptically contoured distributions and propose a robust dominating estimator.     

A revisit to test the equality of variances of several populations

We revisit the problem of testing homoscedasticity (or, equality of variances) of several normal populations which has applications in many statistical analyses, including design of experiments. The standard text books and widely used statistical packages propose a few popular tests including Bartlett's test, Levene's test and a few adjustments of the latter. Apparently, the popularity of these tests have been based on limited simulation study carried out a few decades ago. The traditional tests, including the classical likelihood ratio test (LRT), are asymptotic in nature, and hence do not perform well for small sample sizes. In this paper we propose a simple parametric bootstrap (PB) modification of the LRT, and compare it against the other popular tests as well as their PB versions in terms of size and power. Our comprehensive simulation study bursts some popularly held myths about the commonly used tests and sheds some new light on this important problem. Though most popular statistical software/packages suggest using Bartlette's test, Levene's test, or modified Levene's test among a few others, our extensive simulation study, carried out under both the normal model as well as several non-normal models clearly shows that a PB version of the modified Levene's test (which does not use the F-distribution cut-off point as its critical value), and Loh's exact test are the “best” performers in terms of overall size as well as power.     

A martingale-based test for independence of time to failure and cause of failure for competing risks models

In this article, we introduce a class of tests, using a martingale approach, for testing independence of failure time and cause of failure for competing risks data. Asymptotic distribution of the proposed test statistic is derived. The procedure is illustrated with a real-life data. A simulation study is carried out to assess the level and power of the test.     

论科技英语中wh-words引导名词性从句的用法

科技英语因其自身特点而成为一个独特的语域.wh-words可以用来引导各种从句.文章研究在科技英语中wh-words的句法功能,重点研究wh-words引导名词性从句的用法.运用统计学方法对wh-words在科技英语(T4)等语料库中的分布频率进行分析,根据卡方测试的结果做出判断.wh-words在不同的从句中使用的频率高低不等,有些wh-words在不同的语料库中的分布存在着显著不同,如what等词.因此,在某种程度上可以说,wh-words这一组词的用法特点是科技英语区别于普通英语的一个反映.     

Ban Estimation for Chi-Square Test Criteria in Categorical Data

This expository paper describes some recent work that further develops the theory of BAN estimators and the related chi-scuare test statistics.The extensions are in several directions: (a) the class of regular estimators is broadened by permitting extraneous random elements; (b) more general models are permitted under the constraint equations specification; and (c) BAN estimators are defined for general models combining features of two types of specification.In particular, WLS estimators are shown to be BAN.     

Editor's Report

There are two common methods for statistical inference on 2 × 2 contingency tables. One is the widely taught Pearson chi-square test, which uses the well-known χ²statistic. The chi-square test is appropriate for large sample inference, and it is equivalent to the Z-test that uses the difference between the two sample proportions for the 2 × 2 case. Another method is Fisher’s exact test, which evaluates the likelihood of each table with the same marginal totals. This article mathematically justifies that these two methods for determining extreme do not completely agree with each other. Our analysis obtains one-sided and two-sided conditions under which a disagreement in determining extreme between the two tests could occur. We also address the question whether or not their discrepancy in determining extreme would make them draw different conclusions when testing homogeneity or independence. Our examination of the two tests casts light on which test should be trusted when the two tests draw different conclusions.     

Univaiuate anu multivariate categorical data analysis for block designs

Analysis for univariate and multivariate categorical data in block designs is given and illustrated through examples. The univariate analysis compares the treatments on the basis of their pooled frequency distributions (pooled over blocks). The test statistic used is called Q after Cochran (1950). The large sample null distribution of Q is a chi-square. Analysis of p-variate categorical data (kth variable having ck classes, K=1,...,p) can be done by treating it as a univariate categorical problem with [d] classes. Very often [d] is large in relation to the size of the experiment. This makes the expected frequencies for some of the cells very small, making the univariate method inapplicable. In these circumstances it may be reasonable to compare the treatments on the basis of marginal distributions up to the mth dimension, 1[d] , which is given in this paper. This method is also illustrated for missing observations     

On the distribution of quadratic forms in normal random variables

This paper provides necessary and sufficient conditions for a quadratic form in singular normal random variables to be distributed as a given linear combination of independent noncentral chi-square variables. Using this result, an extension of Cochran's theorem to quadratic forms of noncentral chi-square variables is derived.     

A comparison of confidence intervals generated by the scheffé and bonferroni methods

Simultaneous confidence intervals for the p means of a multivariate normal random variable with known variances may be generated by the projection method of Scheffé and by the use of Bonferroni's inequality. It has been conjectured that the Bonferroni intervals are shorter than the Scheffé intervals, at least for the usual confidence levels. This conjecture is proved for all p≥2 and all confidence levels above 50%. It is shown, incidentally, that for all p≥2 Scheffé's intervals are shorter for sufficiently small confidence levels. The results are also applicable to the Bonferroni and Scheffé intervals generated for multinomial proportions.