Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models

Lin Xue and Liqun Wang
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Lin Xue: Department of Statistics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada

Econometrics, 2024, vol. 12, issue 3, 1-14

Abstract: Regularized regression methods have attracted much attention in the literature, mainly due to its application in high-dimensional variable selection problems. Most existing regularization methods assume that the predictors are directly observed and precisely measured. It is well known that in a low-dimensional regression model if some covariates are measured with error, then the naive estimators that ignore the measurement error are biased and inconsistent. However, the impact of measurement error in regularized estimation procedures is not clear. For example, it is known that the ordinary least squares estimate of the regression coefficient in a linear model is attenuated towards zero and, on the other hand, the variance of the observed surrogate predictor is inflated. Therefore, it is unclear how the interaction of these two factors affects the selection outcome. To correct for the measurement error effects, some researchers assume that the measurement error covariance matrix is known or can be estimated using external data. In this paper, we propose the regularized instrumental variable method for generalized linear measurement error models. We show that the proposed approach yields a consistent variable selection procedure and root-n consistent parameter estimators. Extensive finite sample simulation studies show that the proposed method performs satisfactorily in both linear and generalized linear models. A real data example is provided to further demonstrate the usage of the method.

Keywords: regularization method; penalized estimation; measurement error; instrumental variable; generalized linear model; variable selection; consistency; oracle property (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2024
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