Local linear estimation in partly linear models

Abstract

Let (X, B, Y) denote a random vector such that B and Y are real-valued, and X ∈ ℝ2. Local linear estimates are used in the partial regression method for estimating the regression function E(Y\X, B) = αB + m(X), where α is an unknown parameter, and m(·) is a smooth function. Under appropriate conditions, asymptotic distributions of estimates of α and m(·) are established. Moreover, it is shown that these estimates achieve the best possible rates of convergence in the indicated semi-parametric problems. © 1997 Academic Press.