The T-type estimate of a class of partially non linear models

Abstract

This paper considers a partially non linear model E(Y|X, z, t) = f(X, β) + z^Tg(t) and gives its T-type estimate, which is a weighted quasi-likelihood estimate using sieve method and can be obtained by EM algorithm. The influence functions and asymptotic properties of T-type estimate (consistency and asymptotic normality) are discussed, and convergence rate of both parametric and non parametric components are obtained. Simulation results show the shape of influence functions and prove that the T-type estimate performs quite well. The proposed estimate is also applied to a data set and compared with the least square estimate and least absolute deviation estimate.