ESTIMATION THEORY OF A CLASS OF SEMIPARAMETRIC REGRESSION MODELS

Consider the semiparametric regression model Y=X’β+ g（T） + e, where （X,T） is R×[0,1]-valued random variables, βa p×1 vector of unknown parameter, g an unknown smoothfunction of T in [0,1], e the random error with mean 0 and variance σ>0, possiblyunknown. Assume that e and （X,T） are independent. In this paper, the estimatots ?, gand? of β,g and σ, respectively, based on the combination of nearest neighbor rule and leastsquare rule, are studied. The asymptotic normalities of ? and ? and tbe optimal con-vergence rate of gare obtained under suitable conditions.