Tbs Model For The Semi-parametric Local Linear Estimation

This is a paper for semiparametric regression estimate. Semiparametric regression model is an important statistical model arising from 1980's. The aim of semiparametric methods is to relax the assumptions on the form of a regression function, and to let data search for a suitable function that describes well the available data by allowing the link function to be unknown but smooth. The method (Local polynomial fitting) to estimate the link function is an attractive method both from theoretical and practical point of view. This approach is called nonparametric regression. We begin from the multivariate semiparametric model E(Y|X) = μ(X~Tβ) in this paper, here X is a p-dimensional vector, μ and β are unknown. Since the model is least likely to satisfy the condition: the homogeneity of error's variance and the normality of error's distribution, we transform both Y and μ(X~Tβ) by the same function in order to satisfy the condition of homogeneity and normality. Here we use Box-Cox transform containing parameter A. Finally we estimate the unknown parameters β, λ and the mean function μ(.) using local linear technique and maximum likelihood method through two-step iterated algorithm.