Regression Model With Elliptically Contoured Errors
M. Arashi, A. K. Md E. Saleh, S. M. M. Tabatabaey
TL;DR
This paper compares various estimators for regression models with errors following elliptically contoured distributions, analyzing their risks to identify the most effective approach.
Contribution
It introduces and compares five estimators—LS, RLS, PT, S, and PRS—for regression with ECD errors, highlighting their relative efficiencies.
Findings
Stein-type shrinkage estimators outperform traditional methods in certain conditions.
Restricted least squares offers advantages when restrictions are valid.
Quadratic risk analysis guides estimator selection.
Abstract
For the regression model where the errors follow the elliptically contoured distribution (ECD), we consider the least squares (LS), restricted LS (RLS), preliminary test (PT), Stein-type shrinkage (S) and positive-rule shrinkage (PRS) estimators for the regression parameters. We compare the quadratic risks of the estimators to determine the relative dominance properties of the five estimators.
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Taxonomy
TopicsAdvanced Statistical Methods and Models · Statistical Methods and Inference · Bayesian Methods and Mixture Models