ADAPTIVE VARYING-COEFFICIENT LINEAR MODELS FOR STOCHASTIC PROCESSES: ASYMPTOTIC THEORY

Abstract

We establish the asymptotic theory for the estimation of adaptive varying coefficient linear models. More specifically, we show that the estimator of the index parameter is root-n-consistent. It differs from the locally optimal estimator that has been proposed in the literature with a prerequisite that the estimator is within a n^{-delta} distance of the true value. To this end, we establish two fundamental lemmas for the asymptotic properties of the estimators of parametric components in a general semiparametric setting. Furthermore, the estimation for the coefficient functions is asymptotically adaptive to the unknown index parameter. Asymptotic properties are derived using the empirical process theory for strictly stationary beta-mixing processes.