The estimation of the
slope parameter of the linear regression model with normal error
is considered in this paper when uncertain prior information on
the value of the slope is available. Several alternative
estimators are defined to incorporate both the sample as well as
the non-sample information in the estimation process. Some
important statistical properties of the restricted, preliminary
test, and shrinkage estimators are investigated. The performances
of the estimators are compared based on the criteria of
unbiasedness and mean square error. Both analytical and graphical
methods are explored. None of the estimators is found to be
uniformly superior over the others. However, if the non-sample
information regarding the value of the slope  is close to its true
value, the shrinkage estimator over performs the rest of the
estimators

Hoque, Zahirul

Khan, Shahjahan

Saleh, A. K. Md. Ehsanes

English

University of Southern Queensland ePrints

Developments in decision-theoretic variance estimation,

Inadmissibility of the usual estimator for the mean of a multivariate normal distribution,

Non-optimality of preliminarytest estimators for the mean of a multivariate normal distribution.

Nonparametric estimation of location parameter after a preliminary test on regression.

On biases in estimation due to the use of the preliminary tests of signi¯cance.

On pooling means when variance is unknown.

On the comparison of the pre-test and shrinkage estimators for the univariate normal mean.

On the estimation of the mean vector of Student-t population with uncertain prior information.

Pooling multivariate data.

Prediction Theory for Finite Populations.

Preliminary test estimators of the mean based on p-samples from multivariate Student-t populations.

Shrinkage least squares estimation in a general multivariate linear model.

Shrinkage pre-test estimator of the intercept parameter for a regression model with multivariate Student-t errors.

Estimation of the slope parameter for linear regression model with uncertain prior information

summary The estimation of the slope parameter of the linear regression model with normal error is considered in this paper when uncertain prior information on the value of the slope is available. Several alternative estimators are defined to incorporate both the sample as well as the non-sample informa-tion in the estimation process. Some important statistical properties of the restricted, preliminary test, and shrinkage estimators are investigated. The performances of the estimators are compared based on the criteria of un-biasedness and mean square error. Both analytical and graphical methods are explored. None of the estimators is found to be uniformly superior over the others. However, if the non-sample information regarding the value of the slope is close to its true value, the shrinkage estimator over performs the rest of the estimators

Estimation of the slope parameter for linear regression model with uncertain prior information

Abstract

Similar works

Full text

Available Versions

University of Southern Queensland ePrints

CiteSeerX