Local Linear Estimation in Partly Linear Models

Let (X, B, Y) denote a random vector such thatBandYare real-valued, andX∈R2. Local linear estimates are used in the partial regression method for estimating the regression functionE(Y∣X, B)=αB+m(X), whereαis an unknown parameter, andm(·) is a smooth function. Under appropriate conditions, asymptotic distributions of estimates ofαandm(·) are established. Moreover, it is shown that these estimates achieve the best possible rates of convergence in the indicated semi-parametric problems.