Asymptotic properties in partial linear models under dependence

Consider the regression model y(i) = zeta(i)(T) beta + m(t(i)) + epsilon(i) for i = 1,...,n. Here (zeta(i)(T), t(i))(T) is an element of R-p x [0, 1] are design points, beta is an unknown p x 1 vector of parameters, m is an unknown smooth function from [0, 1] to R and epsilon(i) are the unobserved errors. We will assume that these errors are not independent. Under suitable assumptions, we obtain expansions for the bias and the variance of a Generalized Least Squares (GLS) type regression estimator, and for an estimator of the nonparametric function m((.)). Furthermore, we prove the asymptotic normality of the first estimator. The obtained results axe a generalization of those contained in Speckman (1988), who studied a similar model with i.i.d. error variables.