×

Estimation-equivalent covariance structures for the least squares and MINQUE estimators of the linear model variance. (English) Zbl 1123.62039

Summary: We give a concise alternative derivation of necessary and sufficient conditions on the general nonnegative-definit error covariance structure for the general linear model such that the least squares and the minimum norm quadratic unbiased estimators of the model variance are identical.

MSC:

62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
62H05 Characterization and structure theory for multivariate probability distributions; copulas
Full Text: DOI

References:

[1] Anderson T. W., An Introduction to Multivariate Analysis (1984) · Zbl 0651.62041
[2] DOI: 10.1080/03081088408817616 · Zbl 0552.15009 · doi:10.1080/03081088408817616
[3] Baksalary J. K., Sankhya\={} 42 pp 283– (1980)
[4] Bhimasankaram P., Sankhya\={}. Series A 42 pp 272– (1980)
[5] Graham A., Kronecker Products and Matrix Calculus with Applications (1981) · Zbl 0497.26005
[6] Graybill F. A., Theory and Application of the Linear Model (1976) · Zbl 0371.62093
[7] DOI: 10.1016/S0167-7152(97)00030-8 · Zbl 0888.62057 · doi:10.1016/S0167-7152(97)00030-8
[8] DOI: 10.1016/S0024-3795(00)00033-1 · Zbl 0984.15011 · doi:10.1016/S0024-3795(00)00033-1
[9] Harville D. A., Matrix Algebra from a Statistician’s Perspective (1997) · Zbl 0881.15001
[10] DOI: 10.2307/2685063 · doi:10.2307/2685063
[11] Lewis T. O., Estimation in Linear Models (1971)
[12] DOI: 10.1080/03081087408817070 · doi:10.1080/03081087408817070
[13] Norlèn U., Scand. J. Statist. 2 pp 298– (1975)
[14] DOI: 10.2307/2685062 · doi:10.2307/2685062
[15] Rao , C. R. ( 1967 ). Least squares theory using an estimated dispersion matrix and its applications to measurement of signals . In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1 ). LeCam , L. M. , Neyman , J. eds. Berkeley : University of California Press , 355 – 372 .
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.