Nonparametric checks for single-index models

Details Nonparametric checks for single-index models Nonparametric checks for single-index models

2005-07-21

arxiv.org/abs/math/0507416v1

Annals of Statistics 2005, Vol. 33, No. 3, 1048-1083

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000020 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000020

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.

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