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

Malley, James D.

Softcover

ISBN 10: 0387964495 ISBN 13: 9780387964492

Publisher: Springer, 1986

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 1986
• Language: English
• ISBN 10: 0387964495
• ISBN 13: 9780387964492
• Binding: Paperback
• Number of pages: 156