The Annals of Statistics

Nonparametric checks for single-index models

Winfried Stute and Li-Xing Zhu

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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

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

First available in Project Euclid: 1 July 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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

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