Local Linear Estimation in Partly Linear Models

Let (X, B, Y) denote a random vector such thatBandYare real-valued, andX[set membership, variant]2. Local linear estimates are used in the partial regression method for estimating the regression functionE(Y|X, B)=[alpha]B+m(X), where[alpha]is an unknown parameter, andm(·) is a smooth function. Under appropriate conditions, asymptotic distributions of estimates of[alpha]andm(·) are established. Moreover, it is shown that these estimates achieve the best possible rates of convergence in the indicated semi-parametric problems.