Optimal Unbiased Estimation of Variance Components: 39 (Lecture Notes in Statistics) - Softcover

Malley, James D.

 
9780387964492: Optimal Unbiased Estimation of Variance Components: 39 (Lecture Notes in Statistics)
Softcover
ISBN 10: 0387964495 ISBN 13: 9780387964492
Verlag: Springer, 1986

Inhaltsangabe

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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Reseña del editor

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
1986
Sprache
Englisch
ISBN 10 
0387964495
ISBN 13 
9780387964492
Einband
Tapa blanda
Anzahl der Seiten
160
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
CMN Printpool Inh. Mathis Neumann
https://www.also.com/ec/cms5/en_6000/6000/index.jsp

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Hamburg
Deutschland

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ISBN 10:  3540964495 ISBN 13:  9783540964490
Verlag: Springer-Verlag Berlin and Heide..., 1986
Softcover