MALMEM: model averaging in linear measurement error models

Xinyu Zhang, Yanyuan Ma, Raymond J. Carroll

Research output: Contribution to journalArticle

Abstract

We develop model averaging estimation in the linear regression model where some covariates are subject to measurement error. The absence of the true covariates in this framework makes the calculation of the standard residual-based loss function impossible. We take advantage of the explicit form of the parameter estimators and construct a weight choice criterion. It is asymptotically equivalent to the unknown model average estimator minimizing the loss function. When the true model is not included in the set of candidate models, the method achieves optimality in terms of minimizing the relative loss, whereas, when the true model is included, the method estimates the model parameter with root n rate. Simulation results in comparison with existing Bayesian information criterion and Akaike information criterion model selection and model averaging methods strongly favour our model averaging method. The method is applied to a study on health.

Original languageEnglish (US)
Pages (from-to)763-779
Number of pages17
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume81
Issue number4
DOIs
StatePublished - Jan 1 2019

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Model Averaging
Measurement Error Model
Averaging Method
Loss Function
Covariates
Estimator
Bayesian Information Criterion
Akaike Information Criterion
Model
Asymptotically equivalent
Linear Regression Model
Model Selection
Measurement Error
Optimality
Health
Model averaging
Measurement error
Roots
Unknown
Estimate

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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MALMEM : model averaging in linear measurement error models. / Zhang, Xinyu; Ma, Yanyuan; Carroll, Raymond J.

In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 81, No. 4, 01.01.2019, p. 763-779.

Research output: Contribution to journalArticle

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