Improved Estimation in Measurement Error Models Through Stein Rule Procedure

Abstract

This paper examines the role of Stein estimation in a linear ultrastructural form of the measurement errors model. It is demonstrated that the application of Stein rule estimation to the matrix of true values of regressors leads to the overcoming of the inconsistency of the least squares procedure and yields consistent estimators of regression coefficients. A further application may improve the efficiency properties of the estimators of regression coefficients. It is observed that the proposed family of estimators under some constraint on the characterizing scalar dominates the conventional consistent estimator with respect to the criterion of asymptotic risk under a specific quadratic loss function. Then the problem of prediction of the values of the study variable within the sample is considered, and it is found that the predictors based on the proposed family of estimators are always more efficient than the predictors based on the conventional estimator according to asymptotic predictive mean squared error criterion, although both are biased. Academic PressAMS 1991 subject classifications: 62J07, 62F11.

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

“…Peixe et al (2006) derived the mean squared error of IV estimator under an elliptical distribution of disturbances. Srivastava and Shalabh (1997a,b) and Shalabh (1998Shalabh ( , 2003 reported Downloaded by [Ams/Girona*barri Lib] at 04:00 25 November 2014 some results when the measurement errors are not necessarily normally distributed but without using the set up of exact restrictions and IV estimation. We assume only the existence and finiteness of first four moments of the distributions of measurement errors without associating any particular probability distribution in this article.…”

“…; see Cheng and Van Ness (1999) and Fuller (1987) for more details. In multivariate measurement error models, the availability of covariance matrix of measurement errors or reliability matrix associated with explanatory variables are usually utilized to obtain the consistent estimators of regression coefficients, see for example, Gleser (1992) and Shalabh (1998Shalabh ( , 2003 for more details. Availability of such prior information is a big constraint in obtaining the consistent estimators of parameters; see (Kleeper and Leamer, 1984, p. 163).…”

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

“…Among the different choices available for the additional information to construct the consistent estimators, the use of covariance matrix of measurement errors and reliability matrix associated with explanatory variables, are the popular strategies in case of a multivariate measurement error model -see, for example, [10][11][12][13][14]. So we make use of these two types of information, along with the prior information to construct the estimators of regression coefficients that are consistent and satisfy the given linear restrictions.…”

Improved estimation of regression parameters in measurement error models

“…Thus, Shalabh [21] studied the properties of Stein-type estimator when uu is known. Our study includes a broader class of estimators, such as the preliminary test and the positive-rule Stein-type estimator in addition to the usual Stein-type estimator studied by Shalabh [21] when uu is known.…”