Asymptotic Composite Estimation

Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both estimation efficiency and bias reduction. To this end, a novel method is proposed by utilizing a regression relationship between initial estimators and values of model-independent parameter in an asymptotic sense. The resulting estimators could have smaller limiting variances than those of initial estimators, and for nonparametric regression estimation, could also have faster convergence rate than the classical optimal rate that the corresponding initial estimators can achieve. The simulations are carried out to examine its performance in finite sample situations.