Local Linear Estimation in Partly Linear Models

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)=αβ + 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