Tests of the parallelism of several regression surfaces based on rank- order estimates
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.
scientific article; zbMATH DE number 3988483