an:06943459
Zbl 1407.62145
Zhang, Jun; Feng, Zhenghui; Wang, Xiaoguang
A constructive hypothesis test for the single-index models with two groups
EN
Ann. Inst. Stat. Math. 70, No. 5, 1077-1114 (2018).
00413800
2018
j
62G08 62G10 62G20
empirical residual process; single-index models; local linear smoothing; model checking
Authors' 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.
Fabio Rapallo (Alessandria)