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Testing the equality of linear single-index models. (English) Zbl 1185.62076
Summary: Comparison of nonparametric regression models has been extensively discussed in the literature for the one-dimensional covariate case. The comparison problem largely remains open for completely nonparametric models with multi-dimensional covariates. We address this issue under the assumption that the models are single-index models (SIMs). We propose a test for checking the equality of the mean functions of two (or more) SIMs. The asymptotic normality of the test statistic is established and an empirical study is conducted to evaluate the finite-sample performance of the proposed procedure.

MSC:
62G08 Nonparametric regression and quantile regression
62H15 Hypothesis testing in multivariate analysis
62G20 Asymptotic properties of nonparametric inference
Software:
gss
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