Rank tests in heteroscedastic linear model with nuisance parameters

Abstract

In the linear regression model with heteroscedastic errors, we propose nonparametric tests for regression under nuisance heteroscedasticity, and tests for heteroscedasticity under nuisance regression. Both types of tests are based on suitable ancillary statistics for the nuisance parameters; hence they avoid their estimation, in contradistinction to tests proposed in the literature.

A simulation study, as well as an application of tests to real data, illustrate their good performance.

Keywords

• Heteroscedasticity
• Linear regression
• Rank test
• Regression rank scores
• Signed rank test