Regression rank-scores tests against heavy-tailed alternatives. (English) Zbl 0929.62076

Jurečková, Jana

Bernoulli 5, No. 4, 659-676 (1999).

Summary: Statistical inference in the linear model based on the concept of regression rank scores is invariant to the nuisance regression; hence regression rank-scores tests need no estimation of the nuisance parameters. Such tests, already available in the literature, are manageable, asymptotically distribution-free and have many convenient properties, but they are either censored or applicable only to light-tailed distributions.
To extend the universality of regression rank-scores tests, we propose modified tests applicable to heavy-tailed distributions including Cauchy. Depending on the alternative we want to treat by the test, we censor the score generating function but the censoring is asymptotically negligible. The proposed tests, being asymptotically distribution-free, are as efficient as the ordinary rank tests without nuisance parameters, for a broad class of density shapes.

MSC:

62J05	Linear regression; mixed models
62G10	Nonparametric hypothesis testing
62G20	Asymptotic properties of nonparametric inference

Keywords:

regression quantiles; regression rank test; regression rank scores