Non-standard rank tests
type: Item
instance of: scholarly article
title: Non-standard rank tests
zbMATH Open document ID: 0711.62038
author: David M. Mason
author: Arnold Janssen
published in: Lecture Notes in Statistics
publication date: 1992-09-17T00:00:00Z
review text: The monograph develops a methodology to construct rank tests and to study their asymptotic properties for models where the standard regularity conditions \((L^ 1\)-differentiability of the underlying densities or \(L^ 2\)-differentiability of the square root of the densities) do not hold. Chapter I is devoted to finite sample results for rank tests while the next chapters are mainly concerned with asymptotic properties of rank tests for lifetime models where the underlying random variables are of the form \(X_ i=\gamma (Z_ i+\theta_ 0)+\theta\), \(Z_ i\) are i.i.d. with densities \(f(x)=x^ ar(x)1_{(0,\infty)}(x),\) \(a\geq 0\), with a as the shape parameter and a smooth function r(x) [which \(=(1+a)\exp (- x^{1+a})\) in the Weibull case]. Both parametric models (for \(\theta\)) and semi-parametric models \((\gamma,\theta_ 0,a\) and the function r(x) as nuisance parameter) are considered. The following three null hypotheses are treated: \(H_ 0\) independent and identical distributions, \(H_ 1\) symmetric distributions, \(H_ 2\) independence. Table of Contents: I. Locally most powerful rank-tests - finite sample results (1. Preliminaries; 2. Locally most powerfull rank test for \(H_ 0\); 3. Locally most powerfull rank test for \(H_ 1\); 4. Locally most powerfull rank test for \(H_ 2\) against dependence); II. Asymptotic results for locally most powerful tests (5. Approximate rank tests; 6. Asymptotic results for locally most powerful rank tests with respect to \(H_ 0\); 7. Asymptotic results for \(H_ 1\); 8. Asymptotic results for \(H_ 2\); 9. Asymptotic results for locally most powerful tests in the case \(a=0);\) III. Asymptotic results for rank tests under alternatives (10. Limit distributions under alternatives; 11. Rank tests under almost regular models); IV. Tests based on minimum ranks (12. The minimum rank test (finite sample results); 13. The minimum rank tests (asymptotic results)); V. Parametric results for almost regular models (14. Local asymptotic normal…
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62F03
zbMATH DE Number: 48815
zbMATH Keywords: LAN
zbMATH Keywords: rank tests
zbMATH Keywords: finite sample results
zbMATH Keywords: lifetime models
zbMATH Keywords: parametric models
zbMATH Keywords: semi-parametric models
zbMATH Keywords: nuisance parameter
zbMATH Keywords: symmetric distributions
zbMATH Keywords: independence
zbMATH Keywords: Locally most powerful rank-tests
zbMATH Keywords: Approximate rank tests
zbMATH Keywords: Limit distributions
zbMATH Keywords: almost regular models
zbMATH Keywords: minimum rank test
zbMATH Keywords: Local asymptotic normality
zbMATH Keywords: Monte Carlo results
zbMATH Keywords: Adaptive tests
zbMATH Keywords: regression alternatives
zbMATH Keywords: Monte Carlo approach
zbMATH Keywords: Statistical experiments with non-regular densities
reviewed by: Ryszard Zieliński
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 48815