Testing monotonicity of regression

Testing monotonicity of regression

Subhashis Ghosal, Arusharka Sen, and Aad W. van der Vaart

Source: Ann. Statist. Volume 28, Number 4 (2000), 1054-1082.

Abstract

We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural $U$-process. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that the tests are consistent against general alternatives.

Primary Subjects: 62G08, 62G10

Secondary Subjects: 62G20

Keywords: Empirical process; extreme values; Gaussian process; monotone regression; strong approximation; $U$-process

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aos/1015956707
Mathematical Reviews number (MathSciNet): MR1810919
Digital Object Identifier: doi:10.1214/aos/1015956707
Zentralblatt MATH identifier: 01828974

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