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Linear Models and the Relevant Distributions and Matrix Algebra

Author: David A Harville
Publisher: Boca Raton, FL : CRC Press, [2018]
Series: Texts in statistical science.
Edition/Format:   eBook : Document : English : First editionView all editions and formats
Summary:
"Linear Models and the Relevant Distributions and Matrix Algebra provides in-depth and detailed coverage of the use of linear statistical models as a basis for parametric and predictive inference. It can be a valuable reference, a primary or secondary text in a graduate-level course on linear models, or a resource used (in a course on mathematical statistics) to illustrate various theoretical concepts in the context  Read more...
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Genre/Form: Electronic books
Problems and exercises
Problems, exercises, etc
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David A Harville
ISBN: 9781351264686 1351264680 9781351264662 1351264664
OCLC Number: 1019661144
Description: 1 online resource (xiii, 524 pages).
Contents: Intro; Halftitle; Title page; Copyright page; Table of Contents; Preface; 1 Introduction; 1.1 Linear Statistical Models; 1.2 Regression Models; 1.3 Classificatory Models; 1.4 Hierarchical Models and Random-Effects Models; 1.5 Statistical Inference; 1.6 An Overview; 2 Matrix Algebra: A Primer; 2.1 The Basics; 2.2 Partitioned Matrices and Vectors; 2.3 Trace of a (Square) Matrix; 2.4 Linear Spaces; 2.5 Inverse Matrices; 2.6 Ranks and Inverses of Partitioned Matrices; 2.7 Orthogonal Matrices; 2.8 Idempotent Matrices; 2.9 Linear Systems; 2.10 Generalized Inverses; 2.11 Linear Systems Revisited. 2.12 Projection Matrices2.13 Quadratic Forms; 2.14 Determinants; Exercises; Bibliographic and Supplementary Notes; 3 Random Vectors and Matrices; 3.1 Expected Values; 3.2 Variances, Covariances, and Correlations; 3.3 Standardized Version of a Random Variable; 3.4 Conditional Expected Values and Conditional Variances and Covariances of Random Variables or Vectors; 3.5 Multivariate Normal Distribution; Exercises; Bibliographic and Supplementary Notes; 4 The General Linear Model; 4.1 Some Basic Types of Linear Models; 4.2 Some Specific Types of Gauss-Markov Models (with Examples); 4.3 Regression. 4.4 Heteroscedastic and Correlated Residual Effects4.5 Multivariate Data; Exercises; Bibliographic and Supplementary Notes; 5 Estimation and Prediction: Classical Approach; 5.1 Linearity and Unbiasedness; 5.2 Translation Equivariance; 5.3 Estimability; 5.4 The Method of Least Squares; 5.5 Best Linear Unbiased or Translation-Equivariant Estimation of Estimable Functions (under the G-M Model); 5.6 Simultaneous Estimation; 5.7 Estimation of Variability and Covariability; 5.8 Best (Minimum-Variance) Unbiased Estimation; 5.9 Likelihood-Based Methods; 5.10 Prediction; Exercises. Bibliographic and Supplementary Notes6 Some Relevant Distributions and Their Properties; 6.1 Chi-Square, Gamma, Beta, and Dirichlet Distributions; 6.2 Noncentral Chi-Square Distribution; 6.3 Central and Noncentral F Distributions; 6.4 Central, Noncentral, and Multivariate t Distributions; 6.5 Moment Generating Function of the Distribution of One or More Quadratic Forms or Second-Degree Polynomials (in a Normally Distributed Random Vector); 6.6 Distribution of Quadratic Forms or Second-Degree Polynomials (in a Normally Distributed Random Vector): Chi-Squareness. 6.7 The Spectral Decomposition, with Application to the Distribution of Quadratic Forms6.8 More on the Distribution of Quadratic Forms or Second-Degree Polynomials (in a Normally Distributed Random Vector); Exercises; Bibliographic and Supplementary Notes; 7 Confidence Intervals (or Sets) and Tests of Hypotheses; 7.1 "Setting the Stage": Response Surfaces in the Context of a Specific Application and in General; 7.2 Augmented G-M Model; 7.3 The F Test (and Corresponding Confidence Set) and a Generalized S Method; 7.4 Some Optimality Properties.
Series Title: Texts in statistical science.
Responsibility: David A. Harville.

Abstract:

"Linear Models and the Relevant Distributions and Matrix Algebra provides in-depth and detailed coverage of the use of linear statistical models as a basis for parametric and predictive inference. It can be a valuable reference, a primary or secondary text in a graduate-level course on linear models, or a resource used (in a course on mathematical statistics) to illustrate various theoretical concepts in the context of a relatively complex setting of great practical importance. Features:Provides coverage of matrix algebra that is extensive and relatively self-contained and does so in a meaningful contextProvides thorough coverage of the relevant statistical distributions, including spherically and elliptically symmetric distributionsIncludes extensive coverage of multiple-comparison procedures (and of simultaneous confidence intervals), including procedures for controlling the k-FWER and the FDRProvides thorough coverage (complete with detailed and highly accessible proofs) of results on the properties of various linear-model procedures, including those of least squares estimators and those of the F test. Features the use of real data sets for illustrative purposesIncludes many exercisesDavid Harville served for 10 years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories at Wright-Patterson AFB, Ohio, 20 years as a full professor in Iowa State University's Department of Statistics where he now has emeritus status, and seven years as a research staff member of the Mathematical Sciences Department of IBM's T.J. Watson Research Center. He has considerable relevant experience, having taught M.S. and Ph. D. level courses in linear models, been the thesis advisor of 10 Ph. D. graduates, and authored or co-authored two books and more than 80 research articles. His work has been recognized through his election as a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics and as a member of the International Statistical Institute."--Provided by publisher.

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"The book presents procedures for making statistical inferences on the basis of the classical linear statistical model, and discusses the various properties of those procedures. Supporting material Read more...

 
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