On the characteristic polynomial of the information matrix of balanced fractional \(s^ m\) factorial designs for resolution \(V_{p,q}\)
type: Item
instance of: scholarly article
title: On the characteristic polynomial of the information matrix of balanced fractional \(s^ m\) factorial designs for resolution \(V_{p,q}\)
zbMATH Open document ID: 0629.62081
DOI: 10.1016/0378-3758(88)90020-1
author: Masahide Kuwada
author: Ryuei Nishii
published in: Journal of Statistical Planning and Inference
publication date: 1988-01-01T00:00:00Z
review text: An explicit expression for the characteristic polynomial of the information matrix for a balanced fractional \(s^ m\) factorial design of resolution \(V_{p,q}\) (in particular, when \(p=q=s-1\), of resolution V) is obtained by utilizing the decomposition of a multidimensional relationship algebra into its four two-sided ideals. Furthermore, by use of the algebraic structure of the underlying multidimensional relationship, the trace and the determinant of the covariance matrix of the estimates of effects of interest are derived.
Mathematics Subject Classification ID: 62K15
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 4024563
zbMATH Keywords: balanced arrays
zbMATH Keywords: balanced fractional factorial designs
zbMATH Keywords: explicit expression
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: information matrix
zbMATH Keywords: resolution
zbMATH Keywords: decomposition of a multidimensional relationship algebra
zbMATH Keywords: two-sided ideals
zbMATH Keywords: trace
zbMATH Keywords: determinant
zbMATH Keywords: covariance matrix
MaRDI profile type: Publication
full work available at URL: 0378-3758(88)90020-1
OpenAlex ID: W2083839525
cites work: Q3038435
cites work: Q5511816
cites work: Q3236191
cites work: Optimality of some weighing and \(2^n\) fractional factorial designs
cites work: Q4057439
cites work: Q4124137
cites work: More precise tables of optimal balanced \(2^ m\) fractional factorial designs of Srivastava and Chopra, 7\(\leq m\leq 10\)
cites work: Optimal balanced \(2^7\) fractional factorial designs of resolution \(v\), with \(N\leq 42\)
cites work: Optimal balanced 27fractional factorial designs of resolution V, 49 ≤ N ≤55
cites work: Q4046984
cites work: Q4136368
cites work: Economical Second-Order Designs Based on Irregular Fractions of the 3 n Factorial
cites work: The characteristic polynomial of the information matrix for second-order models
cites work: The Relationship Algebra of an Experimental Design
cites work: Q3844024
cites work: Optimal balanced fractional \(3^m\) factorial designs of resolution V and balanced third-order designs
cites work: Balanced arrays of strength 4 and balanced fractional \(3^m\) factorial designs
cites work: Characteristic polynomials of the information matrices of balanced fractional \(3^ m\) factorial designs of resolution V
cites work: More precise tables of Srivastava-Chopra balanced optimal \(2^ m\) fractional factorial designs of resolution V, m\(\leq 6\)
cites work: Optimal balanced fractional \(2^m\) factorial designs of resolution VII, \(6\leq m\leq 8\)
cites work: Contributions to balanced fractional \(2^m\) factorial designs derived from balanced arrays of strength \(2l\)
cites work: Q5657565
cites work: Q4072674
cites work: On the Characteristic Roots of the Information Matrix of $2^m$ Balanced Factorial Designs of Resolution V, with Applications
cites work: Balanced Optimal 2 m Fractional Factorial Designs of Resolution V, m <= 6
cites work: Q4770972
cites work: Balanced arrays of strength 21 and balanced fractional \(2^m\) factorial designs
cites work: Q4139521
description: scientific article; zbMATH DE number 4024563