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Title: Variable Selection and Estimation in Generalized Linear Measurement Error Models
Abstract:We study the variable selection problem in linear and generalized linear models when some of the predictors are measured with error. We illustrate how measurement error (ME) affects the selection results through an example and propose a regularized instrumental variable (RIV) method to correct for the ME effects. We show that the proposed estimator has the oracle property in a linear model and we derive its asymptotic distribution under general conditions. We also investigate the performance of this estimator in generalized linear models. Our simulation studies show that the RIV estimator outperforms the naive estimator in both linear and generalized linear models. Finally, the proposed method is applied to a real dataset. This is a joint work with Lin Xue.