Analysing exponential family based messy data

Recently exponential family based random effects models have received considerable attention. These models usually arise from an unobservable random process added to the independent exponential family models. An unobservable correlated process, however, would cause correlations among the exponential family based data. This paper, first, develops an asymptotically optimal test for testing the appropriateness of a fixed effects model for the exponential family based independent data versus a random effects model for the exponential family based independent or correlated data. The paper, then, provides a general framework on regression analysis for the exponential family based data generated under the random effects models.     

On the sample breakdown robustness of some nonparametric tests

In this paper, relying on the sample breakdown points, we investigate the sample breakdown properties of some nonparametric tests. It is shown that the sample breakdown points of the sign test asymptotically dominate those of the Wilcoxon test for one–sided hypotheses, However, the different conclusion is derived in the case of testing some shrinking neighborhood hypotheses. The breakdown behaviors of the Kolmogorov test and X²–test are also explored. These studies unify or refine some existing breakdown analyses of tests.     

Kolmogorov-type tests of goodness-of-fit against stochastic ordering

This article addresses the problem of testing the null hypothesis H₀ that a random sample of size n is from a distribution with the completely specified continuous cumulative distribution function F_n(x). Kolmogorov-type tests for H₀ are based on the statistics C⁺ _n = Sup[F_n(x)?F₀(x)] and C^? _n=Sup[F₀(x)?F_n(x)], where F_n(x) is an empirical distribution function. Let F(x) be the true cumulative distribution function, and consider the ordered alternative H₁: F(x)≥F₀(x) for all x and with strict inequality for some x. Although it is natural to reject H₀ and accept H₁ if C ⁺ _n is large, this article shows that a test that is superior in some ways rejects F₀ and accepts H₁ if C^mdash _n is small. Properties of the two tests are compared based on theoretical results and simulated results.     

ON THE NULL DISTRIBUTIONS OF THE ENTROPY TESTS FOR THE GAUSSIAN AND INVERSE GAUSSIAN MODELS

Vasicek [1] Vasicek, O. 1976. A test for normality based on sample entropy. J. R. Statist. Soc. B, 38: 54–59.  [Google Scholar]used the “convolution of twelve uniforms” for a Monte Carlo tabulation of the 5% critical values for his entropy test for normality. We employ a superior normal generator to construct a corrected and extended tabulation for his test. Interestingly, it is shown that, the same tables can be used for implementing Mudholkar and Tian's [2] Mudholkar, G. S. and Tian, L. 1999. “An entropy characterization of the inverse Gaussian distribution and related goodness-of-fit test”. In Tech. Rep., University of Rochester Rochester, NY Submitted for publication [Google Scholar]entropy test for the composite inverse Gaussian hypothesis. The finding extends the known Gaussian, inverse Gaussian analogies.     

PROPERTIES OF THE MINIMUM POINT OF AN UNBALANCED TWO-SIDED RANDOM WALK

In this paper, properties of minimum point of a unbalanced two-sided random walk are investigated. Under the condition that the parameters at both sides tend to zero at the same order, probabilities that the minimum point is on which side, and the second order expansions for the first two moments of the minimum point are obtained. Applications of these results are very promising. First, they can be used to study the properties of the maximum likelihood estimator for the change point in the large sample case; second, they can be used to study inference problems after CUSUM test.     

BIVARIATE DISTRIBUTION WITH TRUNCATED POISSON MARGINAL DISTRIBUTIONS

ABSTRACT

A bivariate distribution, whose marginal distributions are truncated Poisson distributions, is developed as a product of truncated Poisson distributions and a multiplicative factor. The multiplicative factor takes into account the correlation, either positive or negative, between the two random variables. The distributional properties of this model are studied and the model is fitted to a real life bivariate data.     

An exact density-based empirical likelihood ratio test for paired data

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 title, 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. This is particularly true in the cases where there is a nonconstant shift under the alternative or the data distributions are skewed. An extensive Monte Carlo study shows that the proposed test has excellent operating characteristics. We apply the density-based EL ratio test to analyze real data from two medical studies.     

A test for gamma DFR alternative

In this article, a test for exponentiality against gamma DFR alternative based on a quadratic form of the logarithmic observations is proposed. The percentage points and the power of the test are computed through Monte-Carlo simulation. The test is seen to perform well as compared to a chi-square test proposed by Bain and Engelhardt(1975).