Efficient estimation in a semiparametric additive regression model with autoregressive errors

In this paper we characterize and construct efficient estimates of the regression parameter beta in the semiparametric additive regression model Y-j = beta(T)U(j) + gamma(V-j) + X(j), j = 1,2, ... , where beta is an unknown vector in R(m), gamma is an unknown Lipschitz-continuous function from [0, 1] to R, (U-1, V-1), (U-2, V-2), ... are independent R(m) x [0, 1]-valued random vectors with common distribution G and are independent of X(1), X(2), ... , and X(1), X(2), ... is a stationary AR(1) process with parameter alpha belonging to the interval (- 1, 1) and innovation density f with mean 0 and finite variance.