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MALMEM: model averaging in linear measurement error models
Author(s) -
Zhang Xinyu,
Ma Yanyuan,
Carroll Raymond J.
Publication year - 2019
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12317
Subject(s) - akaike information criterion , bayesian information criterion , model selection , mathematics , estimator , information criteria , covariate , residual , statistics , deviance information criterion , linear model , function (biology) , bayesian probability , bayesian inference , algorithm , evolutionary biology , biology
Summary 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.