A0765
Title: Equality between two general ridge estimators and equivalence of their residual sums of squares
Authors: Hirai Mukasa - Kyushu University (Japan) [presenting]
Koji Tsukuda - Kyushu University (Japan)
Abstract: General ridge estimators are typical linear estimators in a general linear model. The class of them includes some shrinkage estimators in addition to classical linear unbiased estimators, such as the ordinary least squares estimator and the generalized least squares estimator. Also, general ridge estimators have some properties, such as linear sufficiency and admissibility in the class of linear estimators. Necessary and sufficient conditions are derived under which two general ridge estimators coincide. In particular, two noteworthy conditions are added to those from previous studies. The first condition corresponds to a celebrated column space relationship condition to the covariance matrix, and the second one is based on the biases of general ridge estimators. Another problem is to derive an equivalence condition such that equality between two residual sums of squares holds when general ridge estimators are considered. Additionally, some concrete examples are demonstrated for which the equivalence conditions hold.
