Asymptotic theory for partly linear models

Abstract

Consider the model , 1≤i≤n. Here x _i = (x _il ,…,x _ip ) and t _i are known and nonrandom design points, β=(β ₁,…,β _p ) is an unknown parameter, g(·) is an unknown function over R ^l, and V _i is a class of linear processes. Based on g(·) estimated by nonparametric kernel estimation or approximated by a finite series expansion, the asymptotic normalities and the strong consistencies of the LS estimator of β and an estimator of are investigated.

Keywords:

• Asymptotic normality
• Strong convergence
• Linear process
• Partly linear model