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Optimal model averaging for partially linear models with missing response variables and error-prone covariates.

Zhongqi Liang1,2, Suojin Wang3, Li Cai4

  • 1School of Data Sciences, Zhejiang University of Finance & Economics, Hangzhou, China.

Statistics in Medicine
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PubMed
Summary
This summary is machine-generated.

This study introduces a new optimal model averaging method for partially linear models with missing data and measurement errors. The proposed approach achieves minimal squared loss, outperforming existing techniques in simulations.

Keywords:
asymptotic optimalitymeasurement errormissing datamodel averagingpartially linear model

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Partially linear models are widely used in statistical modeling.
  • Missing responses and measurement errors in covariates present significant challenges in data analysis.
  • Model averaging aims to improve estimation by combining multiple models.

Purpose of the Study:

  • To develop an optimal model averaging method for partially linear models with missing responses and erroneous covariates.
  • To propose a novel weight choice criterion for model averaging.
  • To establish the asymptotic optimality and convergence properties of the proposed estimator.

Main Methods:

  • A Mallows-type criterion is adapted for weight selection in model averaging.
  • Asymptotic properties of the model averaging estimator are derived under regularity conditions.
  • Local minimization and convergence rates of the weight vector are theoretically established.
  • Simulation studies are conducted to compare the proposed method with existing ones.

Main Results:

  • The proposed model averaging estimator is shown to be asymptotically optimal in terms of minimizing squared loss.
  • The existence and convergence rate of a local minimizing weight vector are proven.
  • Simulation results indicate superior performance of the proposed method over existing approaches.

Conclusions:

  • The novel model averaging technique effectively addresses missing data and measurement error issues in partially linear models.
  • The method provides an asymptotically optimal estimator with desirable theoretical properties.
  • The approach is validated through simulations and demonstrated on an HIV-CD4 dataset.