Determinant efficiencies in ill-conditioned models
type: Item
instance of: scholarly article
title: Determinant efficiencies in ill-conditioned models
zbMATH Open document ID: 1229.62079
DOI: 10.1155/2011/182049
published in: Journal of Probability and Statistics
publication date: 2011-10-26T00:00:00Z
review text: Summary: 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 the 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 \(D_s\) as determinant efficiencies for estimators and their subsets, specifically, \(D_s\)-efficiencies for the constant, linear, pure quadratic, and interactive coefficients in eight known small second-order designs. Studies on \(D\)- and \(D_s\)-efficiencies confirm that designs are seldom efficient for both. Determinant identities demonstrate the propensity for \(D_s\)-inefficient subsets to be masked through near collinearities in overall \(D\)-efficient designs.
Mathematics Subject Classification ID: 62H20
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 5964134
Wikidata QID: Q57444634
author: Donald R. Jensen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/182049
OpenAlex ID: W1989878114
cites work: Q3844024
cites work: Optimum Designs in Regression Problems, II
cites work: Optimum Designs in Regression Problems
cites work: On the Efficient Design of Statistical Investigations
cites work: Factorial Designs, the |X′X| Criterion, and Some Related Matters
cites work: Which Response Surface Design Is Best: A Performance Comparison of Several Types of Quadratic Response Surface Designs in Symmetric Regions
cites work: Response Surface Methodology: 1966-1988
cites work: Q4061810
cites work: Q3922026
cites work: D-Optimality for Regression Designs: A Review
cites work: A generalization of D- and \(D_ 1\)-optimal designs in polynomial regression
cites work: Robust designs for polynomial regression by maximizing a minimum of \(D\)- and \(D_1\)-efficiencies
cites work: On some DS-optimal designs in spherical regions
cites work: On \(D\)-optimal designs for estimating slope
cites work: Q3806614
cites work: Efficient \(D_ s\)-optimal designs for multivariate polynomial regression on the q-cube
cites work: \(D_s\)-optimal designs for polynomial regression using continued fractions
cites work: Some response surface designs for finding optimal conditions
cites work: The Sequential Generation of $D$-Optimum Experimental Designs
cites work: Q5661044
cites work: On a mixture of the \(D\)- and \(D_ 1\)-optimality criterion in polynomial regression
cites work: On Ds-Efeiciency of Some D-Optimal Designs
cites work: Collinearity and least squares regression. With discussion
cites work: RELATIONS BETWEEN TWO SETS OF VARIATES
cites work: Numerical Methods for Computing Angles Between Linear Subspaces
cites work: Q3623845
cites work: Q5561562
cites work: Q5842591
cites work: Hybrid Designs for Quadratic Response Surfaces
cites work: Smallest Composite Designs for Quadratic Response Surfaces
cites work: Q3276963
cites work: Q5806242
cites work: Minimal point second order designs
cites work: Economical Second-Order Designs Based on Irregular Fractions of the 3 n Factorial
cites work: On Minimum-Point Second-Order Designs
cites work: Efficiencies of some small second-order designs
description: scientific article; zbMATH DE number 5964134