Optimal Unbiased Estimation of Variance Components:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1986
|
| Series: | Lecture Notes in Statistics
39 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 notion of quadratic 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 components given by Mitra [1970], and in so doing, provided a mathematical framework for estimation which permitted the immediate application 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 enormous linear model for the components can be displayed as the starting point for many of the popular variance component estimation techniques, thereby unifying the subject in addition to generating answers |
| Physical Description: | 1 Online-Ressource (X, 146 p.) 1 illus |
| ISBN: | 9781461575542 9780387964492 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4615-7554-2 |
Staff View
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Record in the Search Index
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| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781461575542 9780387964492 |
| issn | 0930-0325 |
| language | English |
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| spelling | Malley, James D. Verfasser aut Optimal Unbiased Estimation of Variance Components by James D. Malley New York, NY Springer New York 1986 1 Online-Ressource (X, 146 p.) 1 illus txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 39 0930-0325 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 notion of quadratic 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 components given by Mitra [1970], and in so doing, provided a mathematical framework for estimation which permitted the immediate application 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 enormous linear model for the components can be displayed as the starting point for many of the popular variance component estimation techniques, thereby unifying the subject in addition to generating answers Statistics Statistics, general Statistik Varianzkomponente (DE-588)4132466-3 gnd rswk-swf Schätzung (DE-588)4193791-0 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Varianzkomponente (DE-588)4132466-3 s Schätzung (DE-588)4193791-0 s Optimierung (DE-588)4043664-0 s 1\p DE-604 Lecture Notes in Statistics 39 (DE-604)BV036592911 39 https://doi.org/10.1007/978-1-4615-7554-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Malley, James D. Optimal Unbiased Estimation of Variance Components Lecture Notes in Statistics Statistics Statistics, general Statistik Varianzkomponente (DE-588)4132466-3 gnd Schätzung (DE-588)4193791-0 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4132466-3 (DE-588)4193791-0 (DE-588)4043664-0 |
| title | Optimal Unbiased Estimation of Variance Components |
| title_auth | Optimal Unbiased Estimation of Variance Components |
| title_exact_search | Optimal Unbiased Estimation of Variance Components |
| title_full | Optimal Unbiased Estimation of Variance Components by James D. Malley |
| title_fullStr | Optimal Unbiased Estimation of Variance Components by James D. Malley |
| title_full_unstemmed | Optimal Unbiased Estimation of Variance Components by James D. Malley |
| title_short | Optimal Unbiased Estimation of Variance Components |
| title_sort | optimal unbiased estimation of variance components |
| topic | Statistics Statistics, general Statistik Varianzkomponente (DE-588)4132466-3 gnd Schätzung (DE-588)4193791-0 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Statistics Statistics, general Statistik Varianzkomponente Schätzung Optimierung |
| url | https://doi.org/10.1007/978-1-4615-7554-2 |
| volume_link | (DE-604)BV036592911 |
| work_keys_str_mv | AT malleyjamesd optimalunbiasedestimationofvariancecomponents |