Relative efficiency of higher order norm-based estimator over the least squares estimator

Article Type

Research Article

Publication Title

Communications in Statistics Simulation and Computation

Abstract

In this article, we study the performance of the estimator that minimizes (Formula presented.) based loss function (for (Formula presented.) against the estimator which minimizes the (Formula presented.) order loss function (or the least squares estimator). Commonly occurring examples illustrate the differences in efficiency between (Formula presented.) and (Formula presented.) based estimators. We derive an empirically testable condition under which the (Formula presented.) estimator is more efficient than the least squares estimator. We construct a simple decision rule to choose between (Formula presented.) and (Formula presented.) estimator. Special emphasis is provided to study (Formula presented.) based estimators. A detailed simulation study verifies the effectiveness of this decision rule. Also, the superiority of the (Formula presented.) based estimator is demonstrated in a real life data set. An artificially constructed example that mimics many real life scenarios shows the superiority of (Formula presented.) over (Formula presented.).

DOI

10.1080/03610918.2025.2531157

Publication Date

1-1-2025

Link to Full Text

Share

COinS