Andre I. Khuri

Response Surfaces: Designs and Analyses; Second Edition presents techniques for designing experiments that yield adequate and reliable measurements of one or several responses of interest, fitting and testing the suitability of empirical models used for acquiring information from the experiments, and for utilizing the experimental results to make decisions concerning the system under investigation. This edition contains chapters on response surface models with block effects and on Taguchi's robust parameter design, additional details on transformation of response variable, more material on modified ridge analysis, and new design criteria, including rotatability for multiresponse experiments. It also presents an innovative technique for displaying correlation among several response. Numerical examples throughout the book plus exercises--with worked solutions to selected problems--complement the text.

A thoroughly updated guide to matrix algebra and it uses in statistical analysis and features SAS®, MATLAB®, and R throughout This Second Edition addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole. 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. In addition, André I. Khuri, who has extensive research and teaching experience in the field, joins this new edition as co-author. The Second Edition also: Contains new coverage on vector spaces and linear transformations and discusses computational aspects of matricesCovers the analysis of balanced linear models using direct products of matricesAnalyzes multiresponse linear models where several responses can be of interestIncludes extensive use of SAS, MATLAB, and R throughoutContains over 400 examples and exercises to reinforce understanding along with select solutionsIncludes plentiful new illustrations depicting the importance of geometry as well as historical interludes Matrix Algebra Useful for Statistics, Second Edition is an ideal textbook for advanced undergraduate and first-year graduate level courses in statistics and other related disciplines. The book is also appropriate as a reference for independent readers who use statistics and wish to improve their knowledge of matrix algebra. THE LATE SHAYLE R. SEARLE, PHD, was professor emeritus of biometry at Cornell University. He was the author of Linear Models for Unbalanced Data and Linear Models and co-author of Generalized, Linear, and Mixed Models, Second Edition, Matrix Algebra for Applied Economics, and Variance Components, all published by Wiley. Dr. Searle received the Alexander von Humboldt Senior Scientist Award, and he was an honorary fellow of the Royal Society of New Zealand. ANDRÉ I. KHURI, PHD, is Professor Emeritus of Statistics at the University of Florida. He is the author of Advanced Calculus with Applications in Statistics, Second Edition and co-author of Statistical Tests for Mixed Linear Models, all published by Wiley. Dr. Khuri is a member of numerous academic associations, among them the American Statistical Association and the Institute of Mathematical Statistics.

Given the importance of linear models in statistical theory and experimental research, a good understanding of their fundamental principles and theory is essential. Supported by a large number of examples, Linear Model Methodology provides a strong foundation in the theory of linear models and explores the latest developments in data analysis.After presenting the historical evolution of certain methods and techniques used in linear models, the book reviews vector spaces and linear transformations and discusses the basic concepts and results of matrix algebra that are relevant to the study of linear models. Although mainly focused on classical linear models, the next several chapters also explore recent techniques for solving well-known problems that pertain to the distribution and independence of quadratic forms, the analysis of estimable linear functions and contrasts, and the general treatment of balanced random and mixed-effects models. The author then covers more contemporary topics in linear models, including the adequacy of Satterthwaite’s approximation, unbalanced fixed- and mixed-effects models, heteroscedastic linear models, response surface models with random effects, and linear multiresponse models. The final chapter introduces generalized linear models, which represent an extension of classical linear models.Linear models provide the groundwork for analysis of variance, regression analysis, response surface methodology, variance components analysis, and more, making it necessary to understand the theory behind linear modeling. Reflecting advances made in the last thirty years, this book offers a rigorous development of the theory underlying linear models.

Praise for the First Edition "An enticing approach to the subject. . . . Students contemplating a career in statistics will acquire a valuable understanding of the underlying structure of statistical theory. . . statisticians should consider purchasing it as an additional reference on advanced calculus." –Journal of the American Statistical Association "This book is indeed a pleasure to read. It is simple to understand what the author is attempting to accomplish, and to follow him as he proceeds. . . . I would highly recommend the book for one’s personal collection or suggest your librarian purchase a copy." –Journal of the Operational Research Society Knowledge of advanced calculus has become imperative to the understanding of the recent advances in statistical methodology. The First Edition of Advanced Calculus with Applications in Statistics has served as a reliable resource for both practicing statisticians and students alike. In light of the tremendous growth of the field of statistics since the book’s publication, André Khuri has reexamined his popular work and substantially expanded it to provide the most up-to-date and comprehensive coverage of the subject. Retaining the original’s much-appreciated application-oriented approach, Advanced Calculus with Applications in Statistics, Second Edition supplies a rigorous introduction to the central themes of advanced calculus suitable for both statisticians and mathematicians alike. The Second Edition adds significant new material on: *Basic topological concepts *Orthogonal polynomials *Fourier series *Approximation of integrals *Solutions to selected exercises The volume’s user-friendly text is notable for its end-of-chapter applications, designed to be flexible enough for both statisticians and mathematicians. Its well thought-out solutions to exercises encourage independent study and reinforce mastery of the content. Any statistician, mathematician, or student wishing to master advanced calculus and its applications in statistics will find this new edition a welcome resource.

An advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that relies on linear models with mixed and random effects. This volume covers the most important research of the past decade as well as the latest developments in hypothesis testing. It compiles all currently available results in the area of exact and optimum tests for variance component models and offers the only comprehensive treatment for these models at an advanced level. Statistical Tests for Mixed Linear Models: *Combines analysis and testing in one self-contained volume. *Describes analysis of variance (ANOVA) procedures in balanced and unbalanced data situations. *Examines methods for determining the effect of imbalance on data analysis. *Explains exact and optimum tests and methods for their derivation. *Summarizes test procedures for multivariate mixed and random models. *Enables novice readers to skip the derivations and discussions on optimum tests. *Offers plentiful examples and exercises, many of which are numerical in flavor. *Provides solutions to selected exercises. Statistical Tests for Mixed Linear Models is an accessible reference for researchers in analysis of variance, experimental design, variance component analysis, and linear mixed models. It is also an important text for graduate students interested in mixed models.

Response Surfaces: Designs and Analyses; Second Edition presents techniques for designing experiments that yield adequate and reliable measurements of one or several responses of interest, fitting and testing the suitability of empirical models used for acquiring information from the experiments, and for utilizing the experimental results to make decisions concerning the system under investigation. This edition contains chapters on response surface models with block effects and on Taguchi's robust parameter design, additional details on transformation of response variable, more material on modified ridge analysis, and new design criteria, including rotatability for multiresponse experiments. It also presents an innovative technique for displaying correlation among several response. Numerical examples throughout the book plus exercises--with worked solutions to selected problems--complement the text.