ASYMPTOTIC THEORY FOR PARTLY LINEAR-MODELS

Consider the model Y-i = x(i)(')beta + g(t(i)) + V-i, 1 less than or equal to i less than or equal to n. Here x(i)=(x(il),...,x(ip))' and t(i) are known and nonrandom design points, beta=(beta(1),...,beta(p)) is an unknown parameter, g(.) is an unknown function over R(1), 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 beta and an estimator of sigma(0)(2)=EV(1)(2) are investigated.