Composite estimation: An asymptotically weighted least squares approach

Lu Lin, Feng Li, Kangning Wang, Lixing ZHU

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1367-1393
Number of pages27
JournalStatistica Sinica
Volume29
Issue number3
DOIs
Publication statusPublished - 2019

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Asymptotic representation
  • Composite quantile regression
  • Model-independent parameter
  • Nonparametric regression
  • Weighted least squares

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