Local least product relative error estimation for single-index varying-coefficient multiplicative model with positive responses

Abstract

In this paper, we study the single-index varying-coefficient multiplicative model (SIVCMM) for analyzing data with positive response. Based on the least product relative error (LPRE) and local kernel smoothing methods, an efficient approach is proposed for estimating the unknown parameter vector and nonparametric functions arising in SIVCMM. Furthermore, the convergence properties of the proposed estimators are established. Finally, numerical studies are conducted to test the performance of the proposed approach, and a real data analysis is presented to illustrate the new estimator’s efficiency in practical computation.