Determinant Efficiencies in Ill-Conditioned Models
Author
Source
Journal of Probability and Statistics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-05
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
The canonical correlations between subsets of OLS estimators are identified with 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 concern in 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 between subsets 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-order designs.
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.
American Psychological Association (APA)
Jensen, D. R.. 2011. Determinant Efficiencies in Ill-Conditioned Models. Journal of Probability and Statistics،Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-452475
Modern Language Association (MLA)
Jensen, D. R.. Determinant Efficiencies in Ill-Conditioned Models. Journal of Probability and Statistics No. 2011 (2011), pp.1-15.
https://search.emarefa.net/detail/BIM-452475
American Medical Association (AMA)
Jensen, D. R.. Determinant Efficiencies in Ill-Conditioned Models. Journal of Probability and Statistics. 2011. Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-452475
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-452475