## Nonparametric checks for single-index models.(English)Zbl 1080.62023

Summary: 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.

### MSC:

 62G10 Nonparametric hypothesis testing 62H15 Hypothesis testing in multivariate analysis 62G08 Nonparametric regression and quantile regression 62E17 Approximations to statistical distributions (nonasymptotic) 62G20 Asymptotic properties of nonparametric inference

### Keywords:

maximin tests; omnibus tests; peak alternatives
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### References:

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