Related Research On Semiparametric Product Models

Non-negative data widely exists in the fields of survival analysis,financial economy,biomedicine,so it is widely used in these fields.Multiplicative regression models can deal with such data well,so it is widely used in the analysis and processing of practical problems.Chen et al?2016?^[1]proposed a least product relative errors?LPRE?criterion for the multiplicative regression model,which is a smooth and convex objective function.In this paper,the multiplicative regression model is extended to the single-index varying-coefficient multiplicative model?SIVCMM?and the partially linear multiplicative model?PLMM?,and the application range of positive response variables is extended.The specific research content includes the following two aspects:Based on the LPRE criterion and the local linear smoothing method,a feasible algo-rithm is proposed for estimating the parameter vector and nonparametric functions in the SIVCMM.Under some regular conditions,the asymptotic normality of these estimators are established.Cross-validation and LPRE method are used for selecting the band-width.Finally,numerical simulations and real data analysis illustrate the effectiveness and practicability of the proposed method.For the PLMM,the local linear approximation technique and the LPRE approach are used to study the estimation methods of the parametric and nonparametric parts.Compared with the existing method,the proposed method does not need to provide an initial estimator of the parametric part.Under some regular conditions,the theoretical properties of the proposed estimators are established.Finally,the simulation studies and real data analysis show that our method has satisfactory performance.