Estimation Of Semiparametric Partially Linear Transformation Model

Traditionally,there are two approaches for the estimation of functions in sta-tistical analysis.one is called the parametric approach,the other is nonparametric approach.For example,the estimation of the regression parametre in the linear model we usually meet is of the first.Whatever,we usually use the second for the estimate of the unknown function.This paper is the combination of the two methods.In this paper,we concentrate on the estimation of a semiparametric partially linear transformation model.The basic idea is we give the estimations of the trans-formation coefficient,regression parametre and the unknown function respec-tivelly,then get asympototic properties accordingly.In the process of the estima-tion,we suppose that the transformation coefficient and the regression para-metre are given, we get the estimation of the unknown function using the nonpara-metric method.Then we use the least square critierion to estimate the regression para-metre.After this,we adopt the method of profile likelihood to estimate the transformation coefficient,then studied its properties.Furtherlly,we get properties of regression parametre and the unknown function.In the end,we give the perfor-mance of the finite samples.