## The Annals of Statistics

### Nonparametric checks for single-index models

#### 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

https://projecteuclid.org/euclid.aos/1120224095

Digital Object Identifier
doi:10.1214/009053605000000020

Mathematical Reviews number (MathSciNet)
MR2195628

Zentralblatt MATH identifier
1080.62023

#### 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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