Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-10-01

Journal: ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS

Included Journals: Scopus、SCIE

Volume: 70

Issue: 5

Page Number: 1077-1114

ISSN: 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.