Class Of Rank Tests Research Articles

Rank Test for Testing Randomness of the Technology Parameters in a Stochastic Frontier Regression Model

We propose a class of rank tests for testing the randomness of technology parameters in a stochastic frontier regression model. The asymptotic distribution of the test statistic is derived using the weak convergence results of empirical and rank processes. Since the distribution is quite complex and involves the unknown distribution of the error term, a bootstrap procedure is suggested and its validity is established. Simulation studies indicate that the test works well for most common choices of inefficiency distributions. The proposed test procedure is applied to a data set on electricity utility companies.

Rates of convergence for a class of rank tests for independence

An almost optimal rate of convergence estimate is obtained for a large class of rank statistics for testing independence, including Gini's and Spearman's rank correlation coefficients as well as Spearman's footrule. Bibliography: 18 titles.

The limiting normality of the test statistic for the two-sample problem induced by a convex sum distance

Critchlow (1992, J. Statist. Plann. Inference, 32, 325–346) proposed a method of a unified construction of a class of rank tests. In this paper, we introduce a convex sum distance and prove the limiting normality of the test statistics for the two-sample problem derived by his method.

A class of rank tests for interaction in two-way layouts

A class of aligned rank order tests for interaction in two-way layouts is considered. The technique is based on application of the existing nonparametric techniques for one-way layouts to the transformed observations. It is shown that the asymptotic properties of these techniques are preserved after alignment. Furthermore, asymptotic relative efficiency comparisons are made with some of the competing tests. Finally, we demonstrate that our technique can be used to test for higher-order interactions in general multi-factor layouts.

An extended class of matched pairs tests based on powers of ranks

A large class of rank tests, which includes the familiar sign test and the Wilcoxon signed-ranks test, is described and discussed. This class of distribution-free tests provides a flexible basis for testing research hypotheses of various forms. Exact small sample and approximate large sample procedures are considered. Applications of these procedures are presented, including simple numerical examples.

On asymptotic relative efficiencies of a class of rank tests for independence of two variables

On asymptotic relative efficiencies of a class of rank tests for independence of two variables

Asymptotically Optimal Statistics in Some Models with Increasing Failure Rate Averages

Abstract : Let F and G be defined by F(t) = H(gamma t) and G(t) = H(theta t) where H is unknown and H(O) = O. For testing the equality of the means of F and G in the two-sample problem; it is shown that the Savage (The Annals of Mathematical Statistics (1956) pp 590-615) statistic maximizes the minimum power over increasing failure rate distributions asymptotically. Asymptotic uniqueness holds only in a class of rank tests. The results are extended to censored samples, the problem of estimating the ratio of the means, and the k-sample problem.

On Robust Procedures

Abstract This paper discusses a procedure for finding robust estimators of the location parameter of symmetric unimodal distributions. The estimators are based on robust rank tests and the methods used are applicable to other one parameter problems. To every density function there corresponds an asymptotically most powerful rank test (a.m.p.r.t.). For a set , of density functions the maximin rank test, R, maximizes the minimum limiting Pitman's efficiency of R relative to the a.m.p.r.t. for each member of . This maximin test, R, can be used to construct estimators according to the proposal of Hodges and Lehman; it generates another estimator T in the following manner. If the test based on R is the a.m.p.r.t. for samples from a density function g(x − θ), then the estimator T will be the best linear unbiased estimate (b.l.u.e.) of the location parameter for samples from g(x). Unfortunately, the estimator T is not necessarily consistent for all members of . A class of rank tests which generate linear combina...