Composite estimation: An asymptotically weighted least squares approach

The purpose of this study is three-fold. First, based on an asymptotic presentation of initial estimators and model-independent parameters, either hidden in the model or combined with the initial estimators, a pro forma linear regression between the initial estimators and the parameters is defined in an asymptotic sense. Then, a weighted least squares estimation is constructed within this framework. Second, systematic studies are conducted to examine when both the variance and and the bias can be reduced simultaneously, and when only the variance can be reduced. Third, a generic rule for constructing a composite estimation and unified theoretical properties is introduced. Important examples, such as a quantile regression, nonparametric kernel estimation, and blockwise empirical likelihood estimation, are investigated to explain the methodology and theory. Simulations are conducted to examine the performance of the proposed method in finite sample situations and a real-data set is analyzed as an illustration. Lastly, the proposed method is compared to existing competitors.