Analysis of the positive response data with the varying coefficient partially nonlinear multiplicative model

In this paper, we propose a novel varying coefficient partially nonlinear multiplicative model (VCPNLMM) to handle positive response data in a flexible way. The unknown parameters and functions arising in the model are estimated by a local least product relative error (LLPRE) algorithm which is developed based on the technique of the local kernel smoothing. With the help of quadratic approximation lemma and Lyapunov’s central limit theorem, the convergence properties of the proposed estimators are established. A new goodness-of-fit test is proposed to check whether the coefficient functions are constants or not. Experiments and the real data analysis are conducted to illustrate the performance of the new estimators and testing procedures.