Presentation 2-5, 5:00PM~5:30PM KST.
Speaker
Hirai Mukasa (Kyushu University)
Title
Equality between two general ridge estimators and equivalence of their residual sums of squares.
Abstract
General ridge estimators are typical linear estimators in a general linear model. For example, the ordinary least squares estimator and the weighted least squares estimator are included in the class of them. As a main result, we introduce two types of necessary and sufficient conditions under which two general ridge estimators coincide. The first condition is related to a column space for the covariance matrix of the error term, and the second one is based on the biases of general ridge estimators. We also derive an equivalence condition such that equality between two residual sums of squares holds when general ridge estimators are considered. Additionally, we demonstrate some concrete examples for which the equivalence conditions hold.
This presentation is based on the preprint: Mukasa and Tsukuda (2024, arXiv:2405.20023).