Robust regression estimator for a semiparametric measurement error model with multiple covariates using Monte-Carlo methods

Previous methods for deriving a locally efficient semiparametric estimator for the parameters
in a regression model when some of the covariates are measured with error and no additional assumptions are made on the distribution of covariates, i.e., the so called functional measurement error model, involved solving a difficult ill-posed integral equation which limits the utility of these methods to problems with only a few covariates. In this paper we propose using the Landweber-Fridman regularization scheme for approximating the solution to the integral equation. We show how Monte-Carlo methods can be used to estimate the elements in the Landweber-Fridman regularization algorithm and how stochastic approximation can be implemented together with the Monte-Carlo methods to find the locally efficient estimator. This methodology allows the application of the semiparametric theory to problems that were previously infeasible.

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