ROBUST REGRESSION ESTIMATOR FOR A SEMIPARAMETRIC MEASUREMENT ERROR MODEL WITH MULTIPLE COVARIATES USING MONTE-CARLO METHODS
Keywords:
Functional measurement error model, Ill-posed integral equation, Landweber-Fridman regularization, Locally efficient semiparametric estimator, Stochastic approximation.Abstract
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.
