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

Rameshwar Gupta; Donald Richards

doi:10.1016/0378-3758(85)90026-6

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

Rameshwar Gupta, Donald Richards

Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Tsukanov (Theor. Probab. Appl. 26 (1981) 173-177) considers the regression model E(y|Z)=Fp+Zq, D(y|Z)=σ²I_n, 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 H_p), where H_p 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 language	English (US)
Pages (from-to)	75-80
Number of pages	6
Journal	Journal of Statistical Planning and Inference
Volume	11
Issue number	1
DOIs	https://doi.org/10.1016/0378-3758(85)90026-6
State	Published - Jan 1985

All Science Journal Classification (ASJC) codes

Applied Mathematics
Statistics and Probability
Statistics, Probability and Uncertainty

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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 {\^p}, 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.",

author = "Rameshwar Gupta and Donald Richards",

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AU - Gupta, Rameshwar

AU - Richards, Donald

PY - 1985/1

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N2 - 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.

AB - 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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ER -

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

Abstract

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