Use of prior information in the consistent estimation of regression coefficients in measurement error models

Abstract

A multivariate ultrastructural measurement error model is considered and it is assumed that some prior information is available in the form of exact linear restrictions on regression coefficients. Using the prior information along with the additional knowledge of covariance matrix of measurement errors associated with explanatory vector and reliability matrix, we have proposed three methodologies to construct the consistent estimators which also satisfy the given linear restrictions. Asymptotic distribution of these estimators is derived when measurement errors and random error component are not necessarily normally distributed. Dominance conditions for the superiority of one estimator over the other under the criterion of Löwner ordering are obtained for each case of the additional information. Some conditions are also proposed under which the use of a particular type of information will give a more efficient estimator.