The Annals of Statistics

Nonparametric checks for single-index models

Winfried Stute and Li-Xing Zhu

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Abstract

In this paper we study goodness-of-fit testing of single-index models. The large sample behavior of certain score-type test statistics is investigated. As a by-product, we obtain asymptotically distribution-free maximin tests for a large class of local alternatives. Furthermore, characteristic function based goodness-of-fit tests are proposed which are omnibus and able to detect peak alternatives. Simulation results indicate that the approximation through the limit distribution is acceptable already for moderate sample sizes. Applications to two real data sets are illustrated.

Article information

Source
Ann. Statist., Volume 33, Number 3 (2005), 1048-1083.

Dates
First available in Project Euclid: 1 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1120224095

Digital Object Identifier
doi:10.1214/009053605000000020

Mathematical Reviews number (MathSciNet)
MR2195628

Zentralblatt MATH identifier
1080.62023

Subjects
Primary: 62H15: Hypothesis testing 62G08: Nonparametric regression 62E17: Approximations to distributions (nonasymptotic)

Keywords
Single-index model goodness-of-fit maximin tests omnibus tests peak alternatives

Citation

Stute, Winfried; Zhu, Li-Xing. Nonparametric checks for single-index models. Ann. Statist. 33 (2005), no. 3, 1048--1083. doi:10.1214/009053605000000020. https://projecteuclid.org/euclid.aos/1120224095


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