ESTIMATION THEORY OF A CLASS OF SEMIPARAMETRIC REGRESSION MODELS

<正> Consider the semiparametric regression model Y=X'β+ g（T） + e, where （X,T） is Rp×[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 σ2>0, possiblyunknown. Assume that e and （X,T） are independent. In this paper, the estimatots ?, g_n* and? of β,g and σ2, 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 g_n* are obtained under suitable conditions.