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## Details

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:

## Reviews

*Editorial reviews*

Publisher Synopsis

"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 on matrix algebra and statistical distributions is interspersed with a discussion of relevant inferential procedures and their properties. The coverage ranges from MS-level to advanced researcher. In particular, the material in chapters 6-7 is not covered in an approachable manner in any other books, and greatly generalizes the traditional normal-based linear regression model to the elliptical distributions, thus greatly elucidating the advanced reader on just how far this class of models can be extended. Refreshingly, the material also goes beyond the classical 20th century coverage to include some 21st century topics like microarray (big) data analysis, and control of false discovery rates in large scale experiments...From the point of view of an advanced instructor and researcher on the subject, I very strongly recommend publication...Note that...this book provides the coverage of 3 books, hence the title purporting to provide a 'unified approach' (of 3 related subjects) is indeed accurate." Alex Trindade, Texas Tech University "The book is very well written, with exceptional attention to details. It provides detailed derivations or proofs of almost all the results, and offers in-depth coverage of the topics discussed. Some of these materials (e.g., spherical/elliptical distributions) are hard to find from other sources. Anyone who is interested in linear models should benefit from reading this book and find it especially useful for a thorough understanding of the linear-model theory in a unified framework... The book is a delight to read." Huaiqing Wu, Iowa State University "This book is useful in two ways: an excellent text book for a graduate level linear models course, and for those who want to learn linear models from a theoretical perspective...I genuinely enjoyed reading Ch 1and Ch 4 (Introduction and General Linear Models). Often, the hardest part of teaching linear models from a theoretical perspective is to motivate the students about the utility and generality of such models and the related theory. This book does an excellent job in this area, while presenting a solid theoretical foundation." Arnab Maity, North Carolina State University " . . . the book does a good job of providing background tools of matrix algebra and distribution theory, basic concepts and advanced level theoretical developments of general linear models in a remarkable way and can be recommended both as a textbook to advanced level graduate students and as a reference book to researchers working on theoretical aspects of general linear models and their applications." Anoop Chaturvedi, University of Allahabad "One of Harville's major contributions is that this monograph covers both the requisite linear algebra and the statistical theory in a very thorough and balanced manner. It provides a one-stop source of both the statistical and algebraic information needed for a deep understanding of the linear statistical model. In addition, of course, the large range of "tools" that are introduced and described carefully are invaluable in a many other statistical settings. For these reasons, it has to be compared with some stellar competitors. The seminal books by Rao (1965) and Searle (1971) immediately come to mind. In this reviewer's opinion, Linear Models and the Relevant Distributions and Matrix Algebra, compares with these gems most favourably... In summary, (this) is a first-class volume that will serve as an essential reference for graduate students and established researchers alike in statistics and other related disciplines such as econometrics, biometrics, and psychometrics. As the author discusses, it can also serve as the basis for graduate-level courses which have various emphases. I recommend it strongly. Sometimes you read a book, and you think: 'I wish I had the talent to have written this.' This is definitely one of those books." Statistical Papers "In summary the book does a good job of providing background tools of matrix algebra and distribution theory, basic concepts and advanced level theoretical developments of general linear models in a remarkable way and can be recommended both as a textbook to advanced level graduate students and as a reference book to researchers working on theoretical aspects of general linear models and their applications." Royal Statistical Society Read more...

*User-contributed reviews*