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 Yj = [beta]TUj+[gamma](Vj), J=1,2 ..., where [beta] is an unknown vector in Rm, [gamma] is an unknown Lipschitz-continuous function from [0, 1] to R, (U1, V1), (U2, V2), ... are independent Rm x [0, 1]-valued random vectors with common distribution G and are independent of X1, X2, ..., and X1, X2, ... 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.