The Annals of Statistics

Testing monotonicity of regression

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

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 12 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1015956707

Digital Object Identifier
doi:10.1214/aos/1015956707

Mathematical Reviews number (MathSciNet)
MR1810919

Zentralblatt MATH identifier
1105.62337

Subjects
Primary: 62G08: Nonparametric regression 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties

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

Citation

Ghosal, Subhashis; Sen, Arusharka; van der Vaart, Aad W. Testing monotonicity of regression. Ann. Statist. 28 (2000), no. 4, 1054--1082. doi:10.1214/aos/1015956707. https://projecteuclid.org/euclid.aos/1015956707


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