Consider the regression model for . Here g is an unknown Hölder continuous function of known order p in R, is a parameter vector to be estimated and is an unobserved disturbance. Such a model is often encountered in situations in which there is little real knowledge about the nature of g.
A piecewise polynomial is proposed to approximate g. The least- squares estimator is obtained based on the model . It is shown that can achieve the usual parametric rates with the smallest possible asymptotic variance for the case that X and T are correlated.