Efficient estimation in a semiparametric additive regression model with autoregressive errors

In this paper we characterize and construct efficient estimates of the regression parameter β in the semiparametric additive regression model Yj = βTUj+γ(Vj), j=1,2 …, β is an unknown vector in Rm, γ is an unknown Lipschitz-continuous function from [0, 1] to R, (U1, V1), (U2, V2), … are independent Rm × [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 α belonging to the interval (− 1, 1) and innovation density f with mean 0 and finite variance.