Errors-in-Variables Regression Using Stein Estimates

Abstract

A method is proposed for estimating regression parameters from data containing covariate measurement errors by using Stein estimates of the unobserved true covariates. The method produces consistent estimates for the slope parameter in the classical linear errors-in-variables model and applies to a broad range of nonlinear regression problems, provided the measurement error is Gaussian with known variance. Simulations are used to examine the performance of the estimates in a nonlinear regression problem and to compare them with the usual naive ones obtained by ignoring error and with other estimates proposed recently in the literature.

Key Words:

• Covariate measurement errors
• James-Stein estimates
• M-estimates