Robust Rank Test Research Articles

Rank test of unit‐root hypothesis with AR‐GARCH errors

A robust rank test based on the regression rank score process is proposed to test the unit‐root hypothesis under linear GARCH noises in this article. It is shown that the limit distribution of the rank test is a function of a stable process and a Brownian motion. The finite sample studies indicate that the proposed test statistic exhibits a reliable size and a remarkable power under a variety of tail index , and performs better than other unit‐root tests based on least square procedure, such as the augmented Dick Fuller (ADF) and the Phillips–Perron (PP) tests.

Adaptive linear rank tests for eQTL studies

Expression quantitative trait loci (eQTL) studies are performed to identify single-nucleotide polymorphisms that modify average expression values of genes, proteins, or metabolites, depending on the genotype. As expression values are often not normally distributed, statistical methods for eQTL studies should be valid and powerful in these situations. Adaptive tests are promising alternatives to standard approaches, such as the analysis of variance or the Kruskal-Wallis test. In a two-stage procedure, skewness and tail length of the distributions are estimated and used to select one of several linear rank tests. In this study, we compare two adaptive tests that were proposed in the literature using extensive Monte Carlo simulations of a wide range of different symmetric and skewed distributions. We derive a new adaptive test that combines the advantages of both literature-based approaches. The new test does not require the user to specify a distribution. It is slightly less powerful than the locally most powerful rank test for the correct distribution and at least as powerful as the maximin efficiency robust rank test. We illustrate the application of all tests using two examples from different eQTL studies.

Detecting case–control expression quantitative trait loci using locally most powerful or maximin robust rank tests

In testing genome-wide gene expression quantitative trait loci, efficiency robust statistical methods and their computational convenience are most relevant. For this purpose, we propose to use a modified locally most powerful rank test for the analysis of case-control expression data. This modified rank test statistic is computationally simple, robust for non-normally distributed expression data, and asymptotically locally most powerful. It depends on the specification of a location distribution form for data but is not sensitive to misspecifications. When such a location distribution form cannot be specified, we apply Gastwirth's maximin efficiency robust rank test to gene expression data to maximize the worst Pitman asymptotic relative efficiency among a family of location distributions. We conduct simulation studies to assess their performance and use an application to real data for illustration.

Robust rank tests for k-sample approximate equality in the presence of gross errors

Abstract The probability that a random vector of k-sample rank statistics takes the values in an arbitrary specified Schur-convex set in R k is considered under a k-sample local asymptotic gross error model. When the underlying distributions vary in gross error neighborhoods shrinking at the rate of n−1/2, lower and upper bounds for the limiting probability are obtained by using majorization methods on hyperplanes. These bounds enable us to construct asymptotic level α rank tests for k-sample approximate equality whose acceptance regions are Schur-convex sets, and to give lower bounds for their asymptotic minimum powers. For a class of k-sample rank tests an asymptotic relative efficiency is defined on the basis of the lower bounds and a k-sample robust rank test with a truncated scores generating function is proposed. It is shown that the asymptotic relative efficiency of the proposed rank test coincides with those in one- and two-sample approximate equality derived by Rieder (1981 , Ann. Statist. 9, 245–265). Two-sided robust rank tests for two-sample approximate equality are also considered.

Robust Rank Tests of the Unit Root Hypothesis

We consider a family of rank tests based on the regression rank score process introduced by Gutenbrunner and Jureckova' (1992) to test the unit root hypothesis in economic time series. In contrast to tests based on least squares methods, the rank tests are asymptotically Gaussian under the null hypothesis, and have excellent power-particularly under innovation processes exhibiting heavy tails.

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...