Hypothesis Test For Semiparametric Varying-Coefficient Partially Linear Models

The semi-parametric varying-coefficient partially linear model not only retains the good interpretation of the parametric regression model,but also avoids the curse of dimensionality of the non-parametric regression model,so it has been paid much attention by statisticians.At present,the estimation of the model has been relatively mature.However,there are still many problems to be explored in the practical application of model testing problems.So testing has become a hot spot in contemporary statistical research.This paper focuses on the estimation and testing in the semi-parametric varying-coefficient partially linear model.Firstly,the Profile least square method is used to obtain the estimation of the non-parametric components.Secondly,we construct appropriate statistical test to test the coefficient parameters of the model.After that,under the null hypothesis and appropriate conditions,we prove that the new test statistics follows the standard normal distribution asymptotically.Finally,numerical simulation studies analysis show that the estimation methods and test statistics presented in this paper perform well.