A Mallows-type model averaging estimator for de-noise linear models

Abstract

. This article is concerned with model averaging for de-noise linear models, in which some covariates are not observed, but their ancillary variables are available. The least-squares-based estimation procedure is used to estimate the unknown regression parameter in each candidate model after the calibrated error-prone covariates are obtained. Then a Mallows-type weight choice criterion is constructed. When all candidate models are misspecified, the model averaging estimator is asymptotically optimal in the sense that achieving the lowest possible squared error. On the other hand, when the true model is included in the set of candidate models, the model averaging estimator of the regression parameter is root n consistent. The finite sample performance of our model averaging estimator is evaluated by some simulation studies. The proposed procedure is further applied to real-data analysis.