Estimating Multivariate Variance and Covariance Components Using Quadratic and Bilinear Forms

Estimating Multivariate Variance and Covariance Components Using Quadratic and Bilinear Forms m. 589-808 Biometrica U i ,Cornell University, Itheoe, URA nt Estimating Multivariate Variance and Covariance Components Using Quadratic and Bilinear Forms1 Contribution to disorraajon of “An invarimoe property for t i and sebond order momenta of entimated variance-oovrrianoe oomponenta” by H. Aasws at the lgth ‘ ‘ W o n on Stooh.Stica” Akademie der Wiseensohaften, Berlin, DDR J ~ n a 12,1978 y 1. The Unirariate Case 1.1. The morlel Notation first USMI by FLurrmy and RAO(1967) and many others can be adaphd so aa to write the general linear model for a vector x of N realized v 8 b e of tbe mndom variable X &B (1) X= PI+ 2 Z,bi ill where , i a general mean, 1 is a vector on 8 onea, the bi for i= 1, . . . , c- 1 am u s vectors of qi effects and the Zi &re known matricee, with bc=e,a vector of residual error terms, and Zc= I. For the random effects model (the model used in , tbe AHRENS’ paper, namely EIS&NH~RT’R 11), Model E(bi) 0 , var (bi) 41, and cov ( b ,bi,)= 0 i + i‘ = = with 9; =N http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Biometrical Journal Wiley

Estimating Multivariate Variance and Covariance Components Using Quadratic and Bilinear Forms

Biometrical Journal, Volume 21 (4) – Jan 1, 1979

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Publisher
Wiley
Copyright
Copyright © 1979 WILEY‐VCH Verlag GmbH & Co. KGaA
ISSN
0323-3847
eISSN
1521-4036
DOI
10.1002/bimj.4710210407
Publisher site
See Article on Publisher Site

Abstract

m. 589-808 Biometrica U i ,Cornell University, Itheoe, URA nt Estimating Multivariate Variance and Covariance Components Using Quadratic and Bilinear Forms1 Contribution to disorraajon of “An invarimoe property for t i and sebond order momenta of entimated variance-oovrrianoe oomponenta” by H. Aasws at the lgth ‘ ‘ W o n on Stooh.Stica” Akademie der Wiseensohaften, Berlin, DDR J ~ n a 12,1978 y 1. The Unirariate Case 1.1. The morlel Notation first USMI by FLurrmy and RAO(1967) and many others can be adaphd so aa to write the general linear model for a vector x of N realized v 8 b e of tbe mndom variable X &B (1) X= PI+ 2 Z,bi ill where , i a general mean, 1 is a vector on 8 onea, the bi for i= 1, . . . , c- 1 am u s vectors of qi effects and the Zi &re known matricee, with bc=e,a vector of residual error terms, and Zc= I. For the random effects model (the model used in , tbe AHRENS’ paper, namely EIS&NH~RT’R 11), Model E(bi) 0 , var (bi) 41, and cov ( b ,bi,)= 0 i + i‘ = = with 9; =N

Journal

Biometrical JournalWiley

Published: Jan 1, 1979

References

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