ESTIMATION THEORY OF A CLASS OF SEMIPARAMETRIC REGRESSION-MODELS

Consider the semiparametric regression model Y = X'beta + g(T) + e, where (X,T) is R(P)X [0,1]-valued random variables, beta a p X 1 vector of unknown parameter, g an unknown smooth function of T in [0,1], e the random error with mean 0 and variance sigma-2 > 0, possibly unknown. Assume that e and (X,T) are independent. In this paper, the estimators-beta(n), g(n)* and sigma(n)2 of beta, g and sigma-2, respectively, based on the combination of nearest neighbor rule and least square rule, are studied. The asymptotic normalities of beta(n) 2nd sigma(n)2 and the optimal convergence rate of g(n)* are obtained under suitable conditions.