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  • 1
    Book
    Book
    New York u.a. :Springer,
    UID:
    almahu_BV009706877
    Format: 102 S.
    ISBN: 3-540-94341-2 , 0-387-94341-2
    Series Statement: Lecture notes in statistics 91
    Language: German
    Subjects: Economics , Mathematics
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    Keywords: Jordan-Algebra ; Statistik ; Forschungsbericht
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  • 2
    Book
    Book
    Berlin u.a. :Springer,
    UID:
    almahu_BV000974226
    Format: IX, 146 S.
    ISBN: 3-540-96449-5 , 0-387-96449-5
    Series Statement: Lecture notes in statistics 39.
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    RVK:
    Keywords: Varianzkomponente ; Schätzung ; Optimierung
    URL: Cover
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  • 3
    Online Resource
    Online Resource
    Cambridge :Cambridge University Press,
    UID:
    almafu_9959242021002883
    Format: 1 online resource (xii, 285 pages) : , digital, PDF file(s).
    Edition: 1st ed.
    ISBN: 1-107-21880-2 , 0-511-99432-X , 1-282-97834-9 , 9786612978340 , 0-511-97582-1 , 0-511-99209-2 , 0-511-99312-9 , 0-511-98930-X , 0-511-98752-8 , 0-511-99111-8
    Series Statement: Practical guides to biostatistics and epidemiology
    Content: This book is for anyone who has biomedical data and needs to identify variables that predict an outcome, for two-group outcomes such as tumor/not-tumor, survival/death, or response from treatment. Statistical learning machines are ideally suited to these types of prediction problems, especially if the variables being studied may not meet the assumptions of traditional techniques. Learning machines come from the world of probability and computer science but are not yet widely used in biomedical research. This introduction brings learning machine techniques to the biomedical world in an accessible way, explaining the underlying principles in nontechnical language and using extensive examples and figures. The authors connect these new methods to familiar techniques by showing how to use the learning machine models to generate smaller, more easily interpretable traditional models. Coverage includes single decision trees, multiple-tree techniques such as Random Forests™, neural nets, support vector machines, nearest neighbors and boosting.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , pt. 1. Introduction -- pt. 2. A machine toolkit -- pt. 3. Analysis fundamentals -- pt. 4. Machine strategies. , English
    Additional Edition: ISBN 0-521-69909-6
    Additional Edition: ISBN 0-521-87580-3
    Language: English
    Subjects: Mathematics
    RVK:
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  • 4
    UID:
    b3kat_BV039109575
    Format: XII, 285 S. , Ill., graph. Darst.
    ISBN: 9780521699099 , 0521699096
    Series Statement: Practical guides to biostatistics and epidemiology
    Language: English
    Subjects: Medicine
    RVK:
    Keywords: Biostatistik ; Medizinische Statistik ; Epidemiologie
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  • 5
    Book
    Book
    Berlin u.a. : Springer
    UID:
    b3kat_BV000974226
    Format: IX, 146 S.
    ISBN: 3540964495 , 0387964495
    Series Statement: Lecture notes in statistics 39.
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    RVK:
    Keywords: Varianzkomponente ; Schätzung ; Optimierung
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  • 6
    Online Resource
    Online Resource
    New York, NY :Springer New York,
    UID:
    almahu_9947363091902882
    Format: X, 146 p. 1 illus. , online resource.
    ISBN: 9781461575542
    Series Statement: Lecture Notes in Statistics, 39
    Note: 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 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 Simple Associative 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.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9780387964492
    Language: English
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  • 7
    Online Resource
    Online Resource
    New York, NY :Springer New York,
    UID:
    almahu_9947362838202882
    Format: VII, 102 p. , online resource.
    ISBN: 9781461226789
    Series Statement: Lecture Notes in Statistics, 91
    Content: This monograph brings together my work in mathematical statistics as I have viewed it through the lens of Jordan algebras. Three technical domains are to be seen: applications to random quadratic forms (sums of squares), the investigation of algebraic simplifications of maxi­ mum likelihood estimation of patterned covariance matrices, and a more wide­ open mathematical exploration of the algebraic arena from which I have drawn the results used in the statistical problems just mentioned. Chapters 1, 2, and 4 present the statistical outcomes I have developed using the algebraic results that appear, for the most part, in Chapter 3. As a less daunting, yet quite efficient, point of entry into this material, one avoiding most of the abstract algebraic issues, the reader may use the first half of Chapter 4. Here I present a streamlined, but still fully rigorous, definition of a Jordan algebra (as it is used in that chapter) and its essential properties. These facts are then immediately applied to simplifying the M:-step of the EM algorithm for multivariate normal covariance matrix estimation, in the presence of linear constraints, and data missing completely at random. The results presented essentially resolve a practical statistical quest begun by Rubin and Szatrowski [1982], and continued, sometimes implicitly, by many others. After this, one could then return to Chapters 1 and 2 to see how I have attempted to generalize the work of Cochran, Rao, Mitra, and others, on important and useful properties of sums of squares.
    Note: 1 Introduction -- 2 Jordan Algebras and the Mixed Linear Model -- 2.1 Introductio -- 2.2 Square Matrices and Jordan Algebra -- 2.3 Idempotents and Identity Element -- 2.4 Equivalent Definitions for a Jordan Algebr -- 2.5 Jordan Algebras Derived from Real Symmetric Matrice -- 2.6 The Algebraic Study of Random Quadratic Form -- 2.7 The Statistical Study of Random Quadratic Form -- 2.8 Covariance Matrices Restricted to a Convex Spac -- 2.9 Applications to the General Linear Mixed Mode -- 2.10 A Concluding Exampl -- 3 Further Technical Results on Jordan Algebras -- 3.0 Outline of this Chapte -- 3.1 The JNW Theore -- 3.2 The Classes of Simple, Formally Real, Special Jordan Algebra -- 3.3 The Jordan and Associative Closures of Subsets of Sm -- 3.4 Subspaces of -- 3.5 Solutions of the Equation: sasbs 0 -- 4 Jordan Algebras and the EM Algorithm -- 4.1 Introductio -- 4.2 The General Patterned Covariance Estimation Proble -- 4.3 Precise State of the Proble -- 4.4 The Key Idea of Rubin and Szatrowsk -- 4.5 Outline of the Proposed Metho -- 4.6 Preliminary Result -- 4.7 Further Details of the Proposed Metho -- 4.8 Estimation in the Presence of Missing Dat -- 4.9 Some Conclusions about the General Solutio -- 4.10 Special Cases of the Covariance Matrix Estimation Problem: Zero Constraint -- 4.11 Embeddings for Constant Diagonal Symmetric Matrice -- 4.12 Proof of the Embedding Problem for Sym(m)c -- 4.13 The Question of Nuisance Parameter.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9780387943411
    Language: English
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  • 8
    Online Resource
    Online Resource
    Cambridge :Cambridge University Press,
    UID:
    almahu_9948314492202882
    Format: xii, 285 p. : , ill. (some col.)
    Edition: Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.
    Note: pt. 1. Introduction -- pt. 2. A machine toolkit -- pt. 3. Analysis fundamentals -- pt. 4. Machine strategies.
    Language: English
    Keywords: Electronic books.
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  • 9
    Book
    Book
    New York u.a. : Springer
    UID:
    b3kat_BV009706877
    Format: 102 S.
    ISBN: 3540943412 , 0387943412
    Series Statement: Lecture notes in statistics 91
    Language: German
    Subjects: Economics , Mathematics
    RVK:
    RVK:
    RVK:
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    Keywords: Jordan-Algebra ; Statistik
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