Root-n consistent estimation in partly linear regression models

This paper deals with root-n consistent estimation of the parameter beta in the partly linear regression model Y = beta(T)U + gamma(X) + epsilon, where beta is an element of R(P), gamma is a function on [0, 1](q), the error variable epsilon satisfies E(epsilon\U,X) = O and E(epsilon(2)\U,X) is bounded, and the random vector (U-T,X(T))(T) is R(p) x [0,1](q)-valued. Under an identifiability condition, least squares type estimates of beta are shown to be root-n consistent under mild smoothness assumptions on gamma, h or both, where h(X) E(U\X). No assumption on the distribution of X are imposed. This result improves on a result of Chen (1988).