Optimal Unbiased Estimation Variance (12 results)
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Softcover. Condition: Sehr gut. Berlin, Springer (1986). gr.8°. IX, 146 p. Pbck. Lecture Notes on Statistics, 39.- Throughout browned.
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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, g…enerally 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.
Published by Springer-Verlag, Berlin, 1986
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Seller: J. Wyatt Books, Ottawa, ON, CanadaJ. Wyatt Books
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Add to basketSoftcover. Condition: Very Good. 146 pages in very good condition. Pages are clean and unmarked. Bound in orange and black card covers with black titles. Lightly worn on the edges. VG. Book.
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 160 pp. Englisch.
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Condition: New. Print on Demand pp. 160 67:B&W 6.69 x 9.61 in or 244 x 170 mm (Pinched Crown) Perfect Bound on White w/Gloss Lam.
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Condition: New. PRINT ON DEMAND pp. 160.
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. One: The Basic Model and the Estimation Problem.- 1.1 Introduction.- 1.2 An Example.- 1.3 The Matrix Formulation.- 1.4 The Estimation Criteria.- 1.5 Properties of the Criteria.- 1.6 Selection of Estimation Criteria.-…Two: Basic Linear Technique.- 2.1 Introd.
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -One: The Basic Model and the Estimation Problem.- 1.1 Introduction.- 1.2 An Example.- 1.3 The Matrix Formulation.- 1.4 The Estimation Criteria.- 1.5 Properties of the Criteria.- 1.6 Selection of Estimation Criteria.- Two: Basic Linear T…echnique.- 2.1 Introduction.- 2.2 The vec and mat Operators.- 2.3 Useful Properties of the Operators.- Three: Linearization of the Basic Model.- 3.1 Introduction.- 3.2 The First Linearization.- 3.3 Calculation of var(y).- 3.4 The Second Linearization of the Basic Model.- 3.5 Additional Details of the Linearizations.- Four: The Ordinary Least Squares Estimates.- 4.1 Introduction.- 4.2 The Ordinary Least Squares Estimates: Calculation.- 4.3 The Inner Structure of the Linearization.- 4.4 Estimable Functions of the Components.- 4.5 Further OLS Facts.- Five: The Seely-Zyskind Results.- 5.1 Introduction.- 5.2 The General Gauss-Markov Theorem: Some History and Motivation.- 5.3 The General Gauss-Markov Theorem: Preliminaries.- 5.4 The General Gauss-Markov Theorem: Statement and Proof.- 5.5 The Zyskind Version of the Gauss-Markov Theorem.- 5.6 The Seely Condition for Optimal unbiased Estimation.- Six: The General Solution to Optimal Unbiased Estimation.- 6.1 Introduction.- 6.2 A Full Statement of the Problem.- 6.3 The Lehmann-Scheffé Result.- 6.4 The Two Types of Closure.- 6.5 The General Solution.- 6.6 An Example.- Seven: Background from Algebra.- 7.1 Introduction.- 7.2 Groups, Rings, Fields.- 7.3 Subrings and Ideals.- 7.4 Products in Jordan Rings.- 7.5 Idempotent and Nilpotent Elements.- 7.6 The Radical of an Associative or Jordan Algebra.- 7.7 Quadratic Ideals in Jordan Algebras.- Eight: The Structure of Semisimple Associative and Jordan Algebras.- 8.1 Introduction.- 8.2 The First Structure Theorem.- 8.3 Simple Jordan Algebras.- 8.4 SimpleAssociative Algebras.- Nine: The Algebraic Structure of Variance Components.- 9.1 Introduction.- 9.2 The Structure of the Space of Optimal Kernels.- 9.3 The Two Algebras Generated by Sp( 2).- 9.4 Quadratic Ideals in Sp( 2).- 9.5 Further Properties of the Space of Optimal Kernels.- 9.6 The Case of Sp( 2) Commutative.- 9.7 Examples of Mixed Model Structure Calculations: The Partially Balanced Incomplete Block Designs.- Ten: Statistical Consequences of the Algebraic Structure Theory.- 10.1 Introduction.- 10.2 The Jordan Decomposition of an Optimal Unbiased Estimate.- 10.3 Non-Negative Unbiased Estimation.- Concluding Remarks.- References.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 160 pp. Englisch.
