Optimal Unbiased Estimation of Variance Components (Lecture Notes in Statistics) (v. 39) by James D. Malley

Science & Math | Mathematics
Optimal Unbiased Estimation of Variance Components (Lecture Notes in Statistics) (v. 39)
Title:
Optimal Unbiased Estimation of Variance Components (Lecture Notes in Statistics) (v. 39)
Author:
James D. Malley
ISBN:
0387964495
ISBN13:
978-0387964492
Size PDF:
1529 kb
Size epub:
1440 kb
Publisher:
Springer; Softcover reprint of the original 1st ed. 1986 edition (December 1, 1986)
Language:
English
Other formats:
pdf, odf, mobi, cb7, azw, lit, ibooks
Rating:
3.6
Votes:
344

The clearest way into the Universe is through a forest wilderness. John MuIr As recently as 1970 the problem of obtaining optimal estimates for variance components in a mixed linear model with unbalanced data was considered a miasma of competing, generally weakly motivated estimators, with few firm gUidelines and many simple, compelling but Unanswered questions. Then in 1971 two significant beachheads were secured: the results of Rao [1971a, 1971b] and his MINQUE estimators, and related to these but not originally derived from them, the results of Seely [1971] obtained as part of his introduction of the no~ion of quad­ ratic subspace into the literature of variance component estimation. These two approaches were ultimately shown to be intimately related by Pukelsheim [1976], who used a linear model for the com­ ponents given by Mitra [1970], and in so doing, provided a mathemati­ cal framework for estimation which permitted the immediate applica­ tion of many of the familiar Gauss-Markov results, methods which had earlier been so successful in the estimation of the parameters in a linear model with only fixed effects. Moreover, this usually enor­ mous linear model for the components can be displayed as the starting point for many of the popular variance component estimation tech­ niques, thereby unifying the subject in addition to generating answers.

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