by Debasis Sengupta (Indian Statistical Institute, India) & Sreenivasa Rao Jammalamadaka (University of California, Santa Barbara, USA) Linear Models: An Integrated Approach aims to provide a clear and deep understanding of the general linear model using simple statistical ideas. Elegant geometric arguments are also invoked as needed and a review of vector spaces and matrices is provided to make the treatment self-contained. Complex, matrix-algebraic methods, such as those used in the rank-deficient case, are replaced by statistical proofs that are more transparent and that show the parallels with the simple linear model.
This book has the following special features:
• Use of simple statistical ideas such as linear zero functions and covariance adjustment to explain the fundamental as well as advanced concepts
• Emphasis on the statistical interpretation of complex algebraic results
• A thorough treatment of the singular linear model, including the case of multivariate response
• A unified discussion on models with a partially unknown dispersion matrix, including mixed-effects/variance-components models and models for spatial and time series data
• Insight into updates on the linear model and their connection with diagnostics, design, variable selection, the Kalman filter, etc.
• An extensive discussion on the foundations of linear inference, along with linear alternatives to least squares
• Coverage of other special topics, such as collinearity, stochastic and inequality constraints, misspecified models, etc.
• Simpler proofs of numerous known results
• Pointers to current research through examples and exercises
Contents:
Review of Linear Algebra
Review of Statistical Results
Estimation in the Linear Model
Further Inference in the Linear Model
Analysis of Variance in Basic Designs
General Linear Model
Misspecified or Unknown Dispersion
Updates in the General Linear Model
Multivariate Linear Model
Linear Inference — Other Perspectives
Readership: Researchers, lecturers and postgraduates in statistics and applied mathematics.
“… this book deserves attention from researchers and students in statistics as well as people who are applying linear models and wish to go deeper into parts of the theory. The broad scope of linear model topics covered by the book has a very well-written and unified presentation.”
Mathematical Reviews
“This is an easy-to-read introduction to the theory of linear models, which provide the foundation of regression and analysis of variance.”
Monatshefte für Mathematik
“This monograph can highly be recommended to anyone who is interested in an up-to-date information on linear models.”
Zentralblatt MATH
“One of the important features of this book is the inclusion of a large number of exercises at the end of each chapter. This feature should make the book very valuable to students as well as to teachers … While selected portions of the book can form the basis of an advanced level course in linear models, there is enough material of interest for researchers too.”
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LINEAR MODELS
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