Determinant Efficiencies in Ill-Conditioned Models

Jensen, D. R.

Determinant Efficiencies in Ill-Conditioned Models

dc.contributor.author	Jensen, D. R.	en
dc.contributor.department	Statistics	en
dc.date.accessioned	2017-09-18T09:53:22Z	en
dc.date.available	2017-09-18T09:53:22Z	en
dc.date.issued	2011-10-05	en
dc.date.updated	2017-09-18T09:53:22Z	en
dc.description.abstract	The canonical correlations between subsets of OLS estimators are identifiedwith design linkage parameters between their regressors. Known collinearity indices are extended to encompass angles between each regressor vector and remaining vectors. One such angle quantifies the collinearity of regressors with the intercept, of concernin the corruption of all estimates due to ill-conditioning. Matrix identities factorize a determinant in terms of principal subdeterminants and the canonical Vector Alienation Coefficients between subset estimators—by duality, the Alienation Coefficients betweensubsets of regressors. These identities figure in the study of D and 𝐷𝑠 as determinant efficiencies for estimators and their subsets, specifically, 𝐷𝑠-efficiencies for the constant, linear, pure quadratic, and interactive coefficients in eight known small second-orderdesigns. Studies on D- and 𝐷𝑠-efficiencies confirm that designs are seldom efficient for both. Determinant identities demonstrate the propensity for 𝐷𝑠-inefficient subsets to be masked through near collinearities in overall D-efficient designs.	en
dc.description.version	Published version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	D. R. Jensen, “Determinant Efficiencies in Ill-Conditioned Models,” Journal of Probability and Statistics, vol. 2011, Article ID 182049, 15 pages, 2011. doi:10.1155/2011/182049	en
dc.identifier.doi	https://doi.org/10.1155/2011/182049	en
dc.identifier.uri	http://hdl.handle.net/10919/79026	en
dc.language.iso	en	en
dc.publisher	Hindawi	en
dc.rights	Creative Commons Attribution 4.0 International	en
dc.rights.holder	Copyright © 2011 D. R. Jensen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	en
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	en
dc.title	Determinant Efficiencies in Ill-Conditioned Models	en
dc.title.serial	Journal of Probability and Statistics	en
dc.type	Article - Refereed	en
dc.type.dcmitype	Text	en