A consistent test for the functional form of a regression based on a difference of variance estimators

• 成果类型: Article
• 署名作者: Dette, H
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1018031266
• 发表日期: 1999
• 页码: 1012-1040
• 关键词: Nonparametric regression

摘要

In this paper we study the problem of testing the functional farm of a given regression model. A consistent test is proposed which is based on the difference of the least squares variance estimator in the assumed regression model and a nonparametric variance estimator. The corresponding test statistic can be shown to be asymptotically normal under the null hypothesis and under fixed alternatives with different rates of convergence corresponding to both cases. This provides a simple asymptotic test, where the asymptotic results can also be used for the calculation of the type II error of the procedure at any particular point of the alternative and for the construction of tests for precise hypotheses. Finally, the finite sample performance of the new test is investigated in a detailed simulation study, which also contains a comparison with the commonly used tests.