### Abstract

Tsukanov (Theor. Probab. Appl. 26 (1981) 173-177) considers the regression model E(y|Z)=Fp+Zq, D(y|Z)=σ^{2}I_{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 | |

State | Published - Jan 1 1985 |

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### All Science Journal Classification (ASJC) codes

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability

### Cite this

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*Journal of Statistical Planning and Inference*, vol. 11, no. 1, pp. 75-80. https://doi.org/10.1016/0378-3758(85)90026-6

**Testing optimality of experimental designs for a regression model with random variables.** / Gupta, Rameshwar; Richards, Donald.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Testing optimality of experimental designs for a regression model with random variables

AU - Gupta, Rameshwar

AU - Richards, Donald

PY - 1985/1/1

Y1 - 1985/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=10844265779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10844265779&partnerID=8YFLogxK

U2 - 10.1016/0378-3758(85)90026-6

DO - 10.1016/0378-3758(85)90026-6

M3 - Article

AN - SCOPUS:10844265779

VL - 11

SP - 75

EP - 80

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 1

ER -