The Annals of Statistics

Testing monotonicity of regression

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

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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

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

First available in Project Euclid: 12 March 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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