Testing optimality of experimental designs for a regression model with random variables

Rameshwar Gupta, Donald Richards

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Tsukanov (Theor. Probab. Appl. 26 (1981) 173-177) considers the regression model E(y|Z)=Fp+Zq, D(y|Z)=σ2In, where y(n×1) is a vector of measured values,F(n×k) contains the control variables, Z(n×l) contains the observed values, and p(k×1) and q(l×1) are being estimated. Assuming that Z=FL+R, where L(k×l) is non-random, and the rows of R (n×l) are i.i.d. N(0,Σ), we extend Tsukanov's results by (i) computing E(det Hp), where Hp is the covariance matrix of p̂, the l.s.e. of p, (ii) considering 'optimality in the mean' for the largest root criterion, (iii) discussing these equations when the matrix R has a left-spherical distribution.

Original languageEnglish (US)
Pages (from-to)75-80
Number of pages6
JournalJournal of Statistical Planning and Inference
Volume11
Issue number1
DOIs
StatePublished - Jan 1 1985

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Spherical Distribution
R-matrix
Covariance matrix
Experimental design
Random variables
Design of experiments
Optimality
Regression Model
Random variable
Roots
Testing
Computing
Regression model
Control variable

All Science Journal Classification (ASJC) codes

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

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title = "Testing optimality of experimental designs for a regression model with random variables",
abstract = "Tsukanov (Theor. Probab. Appl. 26 (1981) 173-177) considers the regression model E(y|Z)=Fp+Zq, D(y|Z)=σ2In, where y(n×1) is a vector of measured values,F(n×k) contains the control variables, Z(n×l) contains the observed values, and p(k×1) and q(l×1) are being estimated. Assuming that Z=FL+R, where L(k×l) is non-random, and the rows of R (n×l) are i.i.d. N(0,Σ), we extend Tsukanov's results by (i) computing E(det Hp), where Hp is the covariance matrix of p̂, the l.s.e. of p, (ii) considering 'optimality in the mean' for the largest root criterion, (iii) discussing these equations when the matrix R has a left-spherical distribution.",
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Testing optimality of experimental designs for a regression model with random variables. / Gupta, Rameshwar; Richards, Donald.

In: Journal of Statistical Planning and Inference, Vol. 11, No. 1, 01.01.1985, p. 75-80.

Research output: Contribution to journalArticle

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AU - Richards, Donald

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