Comparing Several Regression Models with Unequal Variances

We consider the problem of comparing k regression models, when the variances are not assumed to be equal. For this problem, the classical F test can lead to misleading results, and there is no simple test which adequately controls the size when the sample sizes are small. For k = 2, the most widely used test is the “weighted F test,” also known as the “asymptotic Chow test.” But this test does not work well for small samples, and various modifications have been proposed in the literature. For k > 2, few tests are available and only the parametric-bootstrap (PB) test of Tian et al. (2009) Tian, L., Ma, C., Vexler, A. (2009). A parametric bootstrap test for comparing heteroscedastic regression models. Communications in Statistics—Simulation and Computation, 38, 1026–1036.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar] controls the size fairly adequately. In this article, we propose three fairly simple F tests which can easily be applied in the general case, k ? 2, and avoid the complications of the PB test. Our simulations indicate that these tests have satisfactory performance. Also, our simulations confirm that the power properties of our proposed tests are similar to the PB test. Therefore, our proposed tests provide simple alternatives to the PB test, which can easily be used by practitioners who may not be familiar with the PB.     

市场的诞生--青海吾屯“唐卡”文化市场的个案研究

古典经济学认为市场诞生于人类的交换秉性。文章以田野工作的方法呈现了转型时期一个少数民族地方性市场的诞生过程,展示出宗教权威、政治权力与传统关系网络在这一过程中的建构性作用。由此认为,市场是一种社会性制度安排,具有天然的社会文化维度。在此基础上,对西方经济学关于市场起源的理论范式进行了反思,并对当前的“市场转型”理论做出部分补充。     

权力形变与资本迁移:发展主义语境下的国家与乡村关系———以四川板村工业园区环境污染纠纷调节机制为例

四川板村工业园区污染事件的处理过程及结果,折射出现代化浪潮之中,农村工业园区管委会、企业以及乡村社会之间的微妙关系,并直指这一关系产生的历史源头与政策支持。主流观点认为,“服务型冶政府确立之后,一系列政策都旨在重建农村、改造农业、造福农民。文章将针对此背景下国家与乡村社会关系的新形式,提出其遵循发展主义逻辑的实质:随着国家权力形态的转变,国家与乡村社会的关系逐渐从通过行政力量的统治直接征取税费,转变为通过推进乡村社会的商品化、工业化,将乡村社会本身纳入商品化的范畴中,并依此完成乡村服务于城市建设乃至国家发展的过程与机制。     

论回族在构建和谐宁夏中的"三力"优势

本文从“回族与生俱来的结合力”、“回族入乡随俗、随遇而安的适应力”、“回族与外族热情沟通的亲和力”三个方面阐述了回族人的性格优势,从中论证了宁夏能够民族和睦、宗教和顺、社会和谐,并使小省区办成了大文化,是与主体少数民族的上述优势密切相关的。回族的“三力”不仅对构建和谐宁夏起着基石作用,对构建整个中国和谐的民族关系也具有现实的借鉴意义。     

A revision of the tukey multiple comparisons procedure to control the probability of committing at most one type i error

Halperin et al. (1988) suggested an approach which allows for k Type I errors while using Scheffe's method of multiple comparisons for linear combinations of p means. In this paper we apply the same type of error control to Tukey's method of multiple pairwise comparisons. In fact, the variant of the Tukey (1953) approach discussed here defines the error control objective as assuring with a specified probability that at most one out of the p(p-l)/2 comparisons between all pairs of the treatment means is significant in two-sided tests when an overall null hypothesis (all p means are equal) is true or, from a confidence interval point of view, that at most one of a set of simultaneous confidence intervals for all of the pairwise differences of the treatment means is incorrect. The formulae which yield the critical values needed to carry out this new procedure are derived and the critical values are tabulated. A Monte Carlo study was conducted and several tables are presented to demonstrate the experimentwise Type I error rates and the gains in power furnished by the proposed procedure     

Simple and Exact Empirical Likelihood Ratio Tests for Normality Based on Moment Relations

The empirical likelihood (EL) technique is a powerful nonparametric method with wide theoretical and practical applications. In this article, we use the EL methodology in order to develop simple and efficient goodness-of-fit tests for normality based on the dependence between moments that characterizes normal distributions. The new empirical likelihood ratio (ELR) tests are exact and are shown to be very powerful decision rules based on small to moderate sample sizes. Asymptotic results related to the Type I error rates of the proposed tests are presented. We present a broad Monte Carlo comparison between different tests for normality, confirming the preference of the proposed method from a power perspective. A real data example is provided.     

Adaptive bootstrap tests and their competitors in the c -sample location problem

This paper deals with a power comparison of different types of tests, parametric, nonparametric, robustified and adaptive ones for the two-sided c -sample location problem. A robustness study on level f in the case of heteroscedasticity and non-normal distributions is included in our study, too. First of all, we consider an adaptive test based on Hogg's concept and two adaptive Bootstrap tests using Hogg's principle. It turns out that the adaptive Hogg-test is the best one in the case of homoscedasticity but for heteroscedasticity, an adaptive Bootstrap test using Hogg's principle is preferable.     

Bayesian estimation and prediction of the intensity of the power law process

In analyzing failure data pertaining to a repairable system, perhaps the most widely used parametric model is a nonhomogeneous Poisson process with Weibull intensity, more commonly referred to as the Power Law Process (PLP) model. Investigations relating to inference of parameters of the PLP under a frequentist framework abound in the literature. The focus of this article is to supplement those findings from a Bayesian perspective, which has thus far been explored to a limited extent in this context. Main emphasis is on the inference of the intensity function of the PLP. Both estimation and future prediction are considered under traditional as well as more complex censoring schemes. Modern computational tools such as Markov Chain Monte Carlo are exploited efficiently to facilitate the numerical evaluation process. Results from the Bayesian inference are contrasted with the corresponding findings from a frequentist analysis, both from a qualitative and a quantitative viewpoint. The developed methodology is implemented in analyzing interval-censored failure data of equipments in a fleet of marine vessels.     

Approximating the distribution of a renewal process using generalized poisson distributions

The exact distribution of a renewal counting process is not easy to compute and is rarely of closed form. In this article, we approximate the distribution of a renewal process using families of generalized Poisson distributions. We first compute approximations to the first several moments of the renewal process. In some cases, a closed form approximation is obtained. It is found that each family considered has its own strengths and weaknesses. Some new families of generalized Poisson distributions are recommended. Theorems are obtained determining when these variance to mean ratios are less than (or exceed) one without having to find the mean and variance. Some numerical comparisons are also made.     

Multiple Decision Procedures for Inference in Regression Models

We consider testing of the significance of the coefficients in the linear model. Unlike in the classical approach, there is no alternative hypothesis to accept when the null hypothesis is rejected. When there is a substantial deviation from the null hypothesis, we reject the null hypothesis and identify based on data alternative hypotheses associated with the independent variables or the levels that contributed most towards the deviation from the null hypothesis.