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

Abstract

a b s t r a c tA 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.

Estimation of Regression Coefficients in a Restricted Measurement Error Model Using Instrumental Variables

“…The ultrastructural model provides a general framework for the study of three interesting models, viz, functional and structural forms of measurement error model as well as classical regression model without measurement errors in a unified manner; see Shalabh et al (2009).…”

“…The problem of consistent estimation of regression coefficients in measurement error models under constraints is discussed by Shalabh et al (2007Shalabh et al ( , 2009 using the covariance matrix of measurement errors associated with explanatory variables. When the covariance matrix of measurement errors is not available, their estimators can not be used.…”

Stochastic Restricted Estimation in Partially Linear Measurement Error Models

“…for the linear measurement error models, Shalabh et al (2007) and Shalabh et al (2009) studied the exact restricted estimation. Shalabh et al (2010) and Li and Yang (2013) studied the estimation of the model when stochastic linear restrictions on regression coefficients are available.…”

A new ridge estimator in linear measurement error model with stochastic linear restrictions

“…Shalabh et al (2007) obtained consistent estimator of regression coefficients in a measurement error model when the prior information is available in the form of exact linear restrictions. In the context of multiple linear regression models, the additional information in the form of known covariance matrix of measurement errors associated with explanatory variables and known matrix of reliability ratios of explanatory variables have been extensively utilized in Shalabh et al (2009). Also, Shalabh et al (2010) obtained consistent estimation of regression coefficients in ultrastructural measurement error model using stochastic prior information.…”