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Indexed by:期刊论文

Date of Publication:2018-10-01

Journal:ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS

Included Journals:SCIE、Scopus

Volume:70

Issue:5

Page Number:1077-1114

ISSN No.:0020-3157

Key Words:Empirical residual process; Single-index models; Local linear smoothing; Model checking

Abstract:Comparison of two-sample heteroscedastic single-index models, where both the scale and location functions are modeled as single-index models, is studied in this paper. We propose a test for checking the equality of single-index parameters when dimensions of covariates of the two samples are equal. Further, we propose two test statistics based on Kolmogorov-Smirnov and Cram,r-von Mises type functionals. These statistics evaluate the difference of the empirical residual processes to test the equality of mean functions of two single-index models. Asymptotic distributions of estimators and test statistics are derived. The Kolmogorov-Smirnov and Cram,r-von Mises test statistics can detect local alternatives that converge to the null hypothesis at a parametric convergence rate. To calculate the critical values of Kolmogorov-Smirnov and Cram,r-von Mises test statistics, a bootstrap procedure is proposed. Simulation studies and an empirical study demonstrate the performance of the proposed procedures.