Bahadur efficiency of the F-test

Extremal problems in large deviations of the F-statistic are considered. It is shown that the slowest rate of convergence over a specified class of distributions of the F-statistic is slower than exponential, and that the Bahadur efficiency of the F-statistic with respect to some distribution-free competitors is identically zero.     

对我国人口迁移信息采集的评述——基于全国人口普查及1%人口抽样调查

通过对历次全国性人口调查中人口迁移信息收集活动的分析发现:人口迁移概念的界定逐步明确,已形成一致的统计口径;在人口信息资料收集中,有关人口迁移内容所占份额越来越大,资料越来越翔实;对于如何收集人口迁移信息在认识上也逐步明确。人口迁移信息资料的丰富与发展,反映了我国统计制度的发展与完善。     

Publication Decisions Revisited: The Effect of the Outcome of Statistical Tests on the Decision to Publish and Vice Versa

This article presents evidence that published results of scientific investigations are not a representative sample of results of all scientific studies. Research studies from 11 major journals demonstrate the existence of biases that favor studies that observe effects that, on statistical evaluation, have a low probability of erroneously rejecting the so-called null hypothesis (H ₀). This practice makes the probability of erroneously rejecting H ₀ different for the reader than for the investigator. It introduces two biases in the interpretation of the scientific literature: one due to multiple repetition of studies with false hypothesis, and one due to failure to publish smaller and less significant outcomes of tests of a true hypotheses. These practices distort the results of literature surveys and of meta-analyses. These results also indicate that practice leading to publication bias have not changed over a period of 30 years.     

Tests of hypotheses on concomitant variables in linear models

The likelihood ratio test for the equality of k univariate normal populations is extended to include the case in which the means are expressed as simple linear regression functions involving two parameters, The moments of the likelihood ratio statistic are derived, and an approximation to the null distribution is obtained.     

On the variance estimate of a wilcoxon-mann whitney statistic for group ordered data

Two consistent estimators for the non-null variance of Wil-coxon-Mann-Whitney’s statistic applied to grouped ordered data, are considered. The first is based on U-statistics and the sec-ond is obtained by the Delta method. Some examples are given to demonstrate the extent of error when using a null variance esti-mate for constructing confidence intervals. It appears that the two consistent estimates are very close, but may both be disting-uishably larger or smaller than the null variance estimate.     

Durbin–Watson and Generalized Durbin–Watson Tests for Autocorrelations and Randomness

The Durbin–Watson (DW) test for lag 1 autocorrelation has been generalized (DWG) to test for autocorrelations at higher lags. This includes the Wallis test for lag 4 autocorrelation. These tests are also applicable to test for the important hypothesis of randomness. It is found that for small sample sizes a normal distribution or a scaled beta distribution by matching the first two moments approximates well the null distribution of the DW and DWG statistics. The approximations seem to be adequate even when the samples are from nonnormal distributions. These approximations require the first two moments of these statistics. The expressions of these moments are derived.     

The degree of severity of heteroskedasticity and the traditional goldfeld and quandt pretest estimator

The traditional Goldfeld and Quandt heteroskedasticity pretesting methodology disregards the fact that even though heteroskedasticity may exist, its degree of severity might be such that the OLS estimator would still outperform the 2SAE. It, therefore, produces results inferior to the OLS estimator when the degree of severity of heteroskedasticity is very mild. This paper through Monte Carlo simulations shows that the probabilistic pretesting procedure suggested by Adjibolosoo (1989) is more powerful than the traditional Goldfeld and Quandt heteroskedasticity pretesting methodology at the usual traditionally selected levels of significance     

Inference under Heteroscedasticity of Unknown Form Using an Adaptive Estimator

The heteroscedasticity consistent covariance matrix estimators are commonly used for the testing of regression coefficients when error terms of regression model are heteroscedastic. These estimators are based on the residuals obtained from the method of ordinary least squares and this method yields inefficient estimators in the presence of heteroscedasticity. It is usual practice to use estimated weighted least squares method or some adaptive methods to find efficient estimates of the regression parameters when the form of heteroscedasticity is unknown. But HCCM estimators are seldom derived from such efficient estimators for testing purposes in the available literature. The current article addresses the same concern and presents the weighted versions of HCCM estimators. Our numerical work uncovers the performance of these estimators and their finite sample properties in terms of interval estimation and null rejection rate.     

Constrained Maximization of the Shapiro–Wilk W Statistic to Estimate Parameters of the Johnson S B Distribution

This article presents a constrained maximization of the Shapiro Wilk W statistic for estimating parameters of the Johnson S _B distribution. The gradient of the W statistic with respect to the minimum and range parameters is used within a quasi-Newton framework to achieve a fit for all four parameters. The method is evaluated with measures of bias and precision using pseudo-random samples from three different S _B populations. The population means were estimated with an average relative bias of less than 0.1% and the population standard deviations with less than 4.0% relative bias. The methodology appears promising as a tool for fitting this sometimes difficult distribution.     

A unified approach to marginal equivalence in the general framework of group invariance

ABSTRACT

Two Bayesian models with different sampling densities are said to be marginally equivalent if the joint distribution of observables and the parameter of interest is the same for both models. We discuss marginal equivalence in the general framework of group invariance. We introduce a class of sampling models and derive marginal equivalence when the prior for the nuisance parameter is relatively invariant. We also obtain some robustness properties of invariant statistics under our sampling models. Besides the prototypical example of v-spherical distributions, we apply our general results to two examples—analysis of affine shapes and principal component analysis.