I believe that there were three books on linear models that were very influential in making the use of matrix algebra routine. Shayle made significant contributions to the successes of C. Henderson, as described in Van Vleck This article points out that Henderson introduced matrix algebra to animal breeding with matrix algebra being introduced to Henderson by Shayle, that Shayle helped with the matrix proof of the equivalence between BLUP and solutions to the mixed- model equations, and highlights the joint paper by Henderson et al.
Jon N. Rao Carleton, Canada. I have some reflections on Shayle Searle. My association with Shayle is mainly through our common interest in linear mixed models theory and practice. However, he helped my Ph. Fawcett with his Ph. In fact he published a joint paper with Fawcett on this topic in Biometrics, I have always admired his immense knowledge of linear models, fixed and mixed, and his dedicated research in this area.
It is nice to see a book giving details of proofs clearly and providing motivation as well. Searle was generous when he felt a particular paper had wide scope and practical importance. He was also pretty tough and critical if he felt a particular method has limited scope. For example, while commenting on my Biometrika paper with H. In my paper, we derived second derivatives of the log likelihood but did not provide an asymptotic variance covariance matrix of ML estimates of variance components.
Searle filled this gap by deriving the asymptotic covariance matrix. I have an indirect connection to Shayle through his fellow countryman Alastair Scott. Alastair and I have collaborated closely for the past 25 years or so on analysis of complex survey data. The GLM procedure is still actively supported. There are however many linear model procedures with different goals.
Shayle also assisted with the exposition of Least Squares Means. LS-means were originally produced by GLM to estimate marginal means over a balanced population. In SAS today LS-means are described as predicted population margins, corresponding to average predicted values in a population where the levels of classification variables are balanced.
In these settings, LS-means are essential to formulating useful hypotheses about group comparisons. In respect of his annotated computer output, Shayle recognized that early SAS output was hard to understand and SAS users benefited from his annotated computer outputs ACOs for various linear models procedures. We have learned some best practices from Shayle. We review all our procedure output presenting a table of parameter least squares means — parameter, estimate, standard error, df, t -value, alphas etc.
Our output now includes graphics with charts of estimate comparisons for parameters and we continue to listen to experts. Thank You Shayle! Dad had been admitted to the hospital for a partially collapsed lung caused from the biopsy earlier that day. He was complaining loudly that the cotton blankets in the hospital were useless and they needed some good old fashion NZ wool blankets.
The surgeon arrived looking like a typical New England doctor, corduroy pants, plaid shirt, comfortable walking shoes with rubber soles for the snow, lab coat and all the trimmings. We greeted him before he entered the room and warned him that Dad was a statistician and that if he wanted to trot out his stats, he did so at his own peril. Dad: Hello - What is your name? How do you pronounce it? Dr: I am going to run a tube into your chest to help get your lung inflated.
I do have one question — What is the probability that I will die during this procedure? It was the third time that day that he had asked that question. Dad had already ripped through the radiologist, the pathologist, the oncologist and a couple of nurses with his probability questions. Dr: The same probability as crossing the street. Dad: Do you know what that probability is? Because I do. Dr: Well not exactly, but I am sure it is very low. Dad: Doctor, how many of these do you do a month?
Dr: Hmmmm, well I probably do one a month. Dad: Do you live around here? Had a busy day? This is the set up, when he lets the Dr think he is done with the number oriented questions - and moves to a more friendly conversation, as friendly as one can be when they are about to get a 18 inch tube inserted in their chest. Dr: small talk Dad: So getting back to your career — how many of these procedures have you done in your career?
Dr: Hmmm , maybe , have not really thought about it — yes I have done of these. Dad: Good. How many years have you been in practice? Dr: 25 years. Dr: To your lung, yes I am pretty close. I have to be close to get the needle in.
Dad: No, pretty close; it is 1. Dr: What is 1. Dad: The number of times a month you have done this procedure over the past 25 years, 1. Dr: looks at me Me: shoulder shrug — Tried to warn you!
Dr: You are really good at math. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible.
After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems.
They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition including a proof , quadratic forms, and Kronecker and Hadamard products. Schott Publisher: Wiley-Interscience ISBN: Category: Mathematics Page: View: A complete, self-contained introduction to matrix analysis theory and practice Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses.
As such, they have become a vital part of any statistical education. Unfortunately, matrix methods are usually treated piecemeal in courses on everything from regression analysis to stochastic processes.
Matrix Analysis for Statistics offers a unique view of matrix analysis theory and methods as a whole. Professor James R. Schott provides in-depth, step-by-step coverage of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors, the Moore-Penrose inverse, matrix differentiation, the distribution of quadratic forms, and more.
Other key features that make this the ideal introduction to matrix analysis theory and practice include: Self-contained chapters for flexibility in topic choice.
Extensive examples and chapter-end practice exercises. Optional sections for mathematically advanced readers. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained. Featuring numerous applied illustrations, numerical examples, and exercises, the book has been updated to include the use of SAS, MATLAB, and R for the execution of matrix computations. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods.
A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized.
A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include: Complex matrices A wide range of special matrices and their properties Special products and operators, such as the Kronecker product Partitioned and patterned matrices Matrix analysis and approximation Matrix optimization Majorization Random vectors and matrices Inequalities, such as probabilistic inequalities Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included.
The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics.
A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject.
The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. Published by Shayle R Searle, New - Hardcover Condition: new.
Book is in NEW condition. Tell us what you're looking for and once a match is found, we'll inform you by e-mail. Can't remember the title or the author of a book? Our BookSleuth is specially designed for you. Item added to your basket View basket.
Proceed to Basket. View basket. Continue shopping. Contact seller Seller Rating:. Free shipping Within U. Seller Image. Matrix Algebra Useful for Statistics. Condition: new. Searle, Shayle R. Create a Want Tell us what you're looking for and once a match is found, we'll inform you by e-mail.
Create a Want BookSleuth Can't remember the title or the author of a book? The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained.
Featuring numerous applied illustrations, numerical examples, and exercises, the book has. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future.
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