Shrinkage estimator of regression model under asymmetric loss

ABSTRACT

This article investigates the performance of the shrinkage estimator (SE) of the parameters of a simple linear regression model under the LINEX loss criterion. The risk function of the estimator under the asymmetric LINEX loss is derived and analyzed. The moment-generating functions and the first two moments of the estimators are also obtained. The risks of the SE have been compared numerically with that of pre-test and least-square estimators (LSEs) under the LINEX loss criterion. The numerical comparison reveals that under certain conditions the LSE is inadmissible, and the SE is the best among the three estimators.

KEYWORDS:

• Linear regression
• Normal error
• Shrinkage estimator
• Pre-test estimator
• LINEX loss and risk function

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62C12, 62C15
• Secondary 62F10