Resumen de Asymptotic properties in partial linear models under dependence

Alejandro Quintela-del-Río , Germán Aneiros Pérez

• Consider the regression model yi=\zetaiT\beta+m(ti)+\varepsiloni for i=1,...,n. Here (\zetaiT,ti)T\in Rp x [0,1] are design points, \beta is an unknown px1 vector of parameters, m is an unknown smooth function of [0,1] in R and \varepsiloni are the unobserved disturbances. 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 parameter estimator and for an estimator of the nonparametric part m( ). Furthermore, we prove the asymptotic normality of the first one. The obtained results are a generalization of those obtained by Speckman (1988), who studied a similar model with i.i.d. error variables