A note on constrained estimation in the simple linear measurement error model

Abstract

It is well known that for any sample size the estimator for the slope in the simple linear measurement error model does not possess even a first moment. Addressing this issue constrained maximum likelihood estimators (MLEs) are developed using three different approaches, under a number of identifiability assumptions. The constrained MLEs have finite moments of all orders. They are asymptotically equivalent to the MLE, which is known to be consistent and asymptotically normal. Numerical investigation shows that the constrained MLEs perform well under a wide variety of experimental settings.