A tow-stage procedure for testing homogeneity of means against ordered alternatives in analysis of variance with unequal variances

In this paper we present a two-stage sampling procedure for testing the equality of normal means against ordered alternatives in one-way analysis of variance with unequal unknown variances. A table of approximated percentiles needed for implementation is provided. Some Monte Carlo results for estimating the power of the proposed test statistic are presented.     

On hypothesis testing for Poisson processes. Singular cases

ABSTRACT

We consider the problem of hypothesis testing in the situation where the first hypothesis is simple and the second one is local one-sided composite. Wedescribe the choice of the thresholds and the power functions of different tests when the intensity function of the observed inhomogeneous Poisson process has two different types of singularity: cusp and discontinuity. The asymptotic results are illustrated by numerical simulations.     

A modified Mack–Wolfe test for the umbrella alternative problem

ABSTRACT

The Mack–Wolfe test is the most frequently used non parametric procedure for the umbrella alternative problem. In this paper, modifications of the Mack–Wolfe test are proposed for both known peak and unknown peak umbrellas. The exact mean and variance of the proposed tests in the null hypothesis are also derived. We compare these tests with some of the existing tests in terms of the type I error rate and power. In addition, a real data example is presented.     

Stabilizing the Performance of Kurtosis Estimator of Multivariate Data

The estimation of the kurtosis parameter of the underlying distribution plays a central role in many statistical applications. The central theme of the article is to improve the estimation of the kurtosis parameter using a priori information. More specifically, we consider the problem of estimating kurtosis parameter of a multivariate population when some prior information regarding the the parameter is available. The rationale is that the sample estimator of the kurtosis parameter has a large estimation error. In this situation we consider shrinkage and pretest estimation methodologies and reappraise their statistical properties. The estimation based on these strategies yield relatively smaller estimation error in comparison with the sample estimator in the candidate subspace. A large sample theory of the suggested estimators are developed and compared. The results demonstrate that suggested estimators outperform the estimator based on the sample data only in the candidate subspace. In an effort to appreciate the relative behavior of the estimators in a finite sample scenario, a Monte-carlo simulation study is planned and performed. The result of simulation study strongly corroborates the asymptotic result. To illustrate the application of the estimators, some example are showcased based on recently published data.     

On the estimation of reliabilty function in a Weibull lifetime distribution

The estimation of the reliability function of the Weibull lifetime model is considered in the presence of uncertain prior information (not in the form of prior distribution) on the parameter of interest. This information is assumed to be available in some sort of a realistic conjecture. In this article, we focus on how to combine sample and non-sample information together in order to achieve improved estimation performance. Three classes of point estimatiors, namely, the unrestricted estimator, the shrinkage estimator and shrinkage preliminary test estimator (SPTE) are proposed. Their asymptotic biases and mean-squared errors are derived and compared. The relative dominance picture of the estimators is presented. Interestingly, the proposed SPTE dominates the unrestricted estimator in a range that is wider than that of the usual preliminary test estimator. A small-scale simulation experiment is used to examine the small sample properties of the proposed estimators. Our simulation investigations have provided strong evidence that corroborates with asymptotic theory. The suggested estimation methods are applied to a published data set to illustrate the performance of the estimators in a real-life situation.     

A Proportional Random Utility Approach to Qualitative Response Models

A new functional form of the response probability for a qualitative response model is proposed. The new model is flexible enough to avoid the constraint of independence from irrelevant alternatives, which is perceived as a weakness of the multinomial logit model in some applications. It is computationally simpler than the multinomial probit model and is promising for analyzing problems with a moderate number of alternatives.     

Bootstrap tests for multivariate directional alternatives

Tests on multivariate means that are hypothesized to be in a specified direction have received attention from both theoretical and applied points of view. One of the most common procedures used to test this cone alternative is the likelihood ratio test (LRT) assuming a multivariate normal model for the data. However, the resulting test for an ordered alternative is biased in that the only usable critical values are bounds on the null distribution. The present paper provides empirical evidence that bootstrapping the null distribution of the likelihood ratio statistic results in a bootstrap test (BT) with comparable power properties without the additional burden of assuming multivariate normality. Additionally, the tests based on the LRT statistic can reject the null hypothesis in favor of the alternative even though the true means are far from the alternative region. The BT also has similar properties for normal and nonnormal data. This anomalous behavior is due to the formulation of the null hypothesis and a possible remedy is to reformulate the null to be the complement of the alternative hypothesis. We discuss properties of a BT for the modified set of hypotheses (MBT) based on a simulation study. The resulting test is conservative in general and in some specific cases has power estimates comparable to those for existing methods. The BT has higher sensitivity but relatively lower specificity, whereas the MBT has higher specificity but relatively lower sensitivity.     

Pooling reliability functions

In this article large sample pooling procedures for reliability functions of an exponential life testing model is considered. Asymptotic properties of shrinkage estimation procedure subsequent to preliminary tests are developed. It is shown that the proposed estimator possesses substantially snakker asymptotic mean squared error than the usual estimator in a region of the lparameter space. Relative efficiencies of the purposed estimators to the usual estimators are obtained and recommendations of the level of the preliminary tests are provided. Relative dominance picture of the estimators is presented. It is shown that the proposed estimator provides a wider dominance range over usual estimator than the usual preliminary test estimator. More importantly, the size of the preliminary test is meaningful. Simulation studies is also carried out to appraise the performance of the estimators when samples are small.     

The Multivariate Randomized Complete Block Design: A Novel Permutation Solution in Case of Ordered Categorical Variables

In this article, multivariate extensions of the combination-based test statistics for the comparison of several treatments in the multivariate Randomized Complete Block designs are introduced in case of categorical response variables. Several tests for the multivariate Randomized Complete Block designs, including MANOVA procedure, are compared with the method proposed via a Monte Carlo simulation study. The method has also been applied to a real case study in the field of sensorial testing studies. Results suggest that in each experimental situation where normality of the supposed underlying continuous model is hard to justify and especially when errors have heavy-tailed distributions, the proposed nonparametric procedure can be considered as a valid solution.     

A model of uniform association plus two-diagonalsparameter and its application to occupational mobility table data

For the analysis of square contingency tables with ordered categories, Agresti (1988) introduced a model having the structure of uniform association plus a main-diagonal parameter. This paper extends that model. The extended model has the structure of uniform association plus two-diagonals-parameter, and it is a special case of the quasi-uniform association model introduced by Goodman (1979). The Danish occupational mobility table data are analyzed using the models introduced here.