Semiparametric Additive Regression
针对模型y = x'β + g(t) + 误差，其中g未知但光滑，提出一种简单估计量，证明其n^{1/2}一致性，并在误差分布已知时达到Hajek-LeCam下界。
SUMMARY A simple estimator for β is proposed for the model y = x'β + g(t)+ error, g smooth but unknown. The approach is to approximate the estimating equation obtained from a ***semiparametric likelihood and in the simplest case reduces to minimizing the distance between the 'pseudoresiduals' y - x'β and a local linear cross-validated estimate of them. When the errors are independent with finite variance, the bias and variance of the estimate are computed and compared against the least squares estimate with g known. It is shown that n 1/2-consistent estimates are possible when the bandwidth contains only a finite number of points and their asymptotic relative efficiency is computed in special cases. When the error distribution is known up to a scale factor and the design points (X, T) are assumed to be drawn as independent samples from a bivariate distribution, the Hajek-LeCam lower bound for the variance of any regular estimator of β is computed and a sequence of estimators is exhibited which achieves this bound. When X and T are independent these estimators do as well asymptotically as the maximum likelihood estimator with g known.