Tests of the parallelism of several regression surfaces based on rank- order estimates
type: Item
instance of: scholarly article
title: Tests of the parallelism of several regression surfaces based on rank- order estimates
zbMATH Open document ID: 0611.62045
DOI: 10.1016/0378-3758(86)90174-6
author: Ching-Yuan Chiang
published in: Journal of Statistical Planning and Inference
publication date: 1986-01-01T00:00:00Z
review text: The author considers two or more (s\(\geq 2)\) linear regression models \(X_{k_ i}=\alpha_ k+\beta_ kc_{k_ i}+\epsilon_{k_ i}\), \(k=1,...,s\); \(i=1,...,n_ k\), where each \(\alpha_ k\in {\mathbb{R}}\) is an unknown intercept, \(\beta_ k\) is a q-dimensional vector of unknown parameters, \(c_{k_ i}\) is a q-dimensional vector of known constants, and all the \(\epsilon_{k_ i}'s\) are i.i.d. with distribution function F. The problem is to test \(H_ 0: \beta_ 1=\beta_ 2=...=\beta_ s=\beta\) (unknown) vs. \(H_ 1: \beta_ k\neq \beta_ j\) for some \(1\leq k\neq j\leq s\). Tests of Wald-type are presented. The tests based on a quadratic form in rank-order estimates of the regression parameters are asymptotically distribution-free. They are compared with classical parametric tests; the asymptotic relative efficiencies are given.
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 3988483
zbMATH Keywords: Wald-type tests
zbMATH Keywords: classical normal theory test
zbMATH Keywords: general likelihood ratio test
zbMATH Keywords: aligned rank-order tests
zbMATH Keywords: asymptotic optimality
zbMATH Keywords: parallelism
zbMATH Keywords: quadratic form
zbMATH Keywords: rank-order estimates
zbMATH Keywords: regression parameters
zbMATH Keywords: asymptotically distribution-free
zbMATH Keywords: asymptotic relative efficiencies
MaRDI profile type: Publication
full work available at URL: 0378-3758(86)90174-6
OpenAlex ID: W2028780444
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description: scientific article; zbMATH DE number 3988483