Semi-parametric Model Estimates And Inspection

As an important part of semi-parameter models, Varying Coefficient Models have been deeply studied in theory. Right now there have been a couple of methods proposed to estimate the unknown parameter function, but most of these methods are based on the assumption of homoscedasticity of the model. There are some of methods do assume the situation of heteroscedasticity, but they do not provide efficient estimations of the unequal variances. This article firstly studied a class of heteroscedastic varying coefficient models, provided efficient estimations for the model based on local weighted linear method, and test the estimations by non-parametric method. Upon this foundation, this article also studied the estimation problems for partially linear varying coefficient models under heteroscedasticity.