Linear Models: An Integrated Approach

An Integrated Approach

S Rao Jammalamadaka, Debasis Sengupta

• Publisher: World Scientific
• Year: 2003
• Print ISBN: 9789810245924, 9789810245924
• eBook ISBN: 9789812564900
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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

Table of contents

• Preface
• Contents
• Glossary of Abbreviations
• Glossary of Matrix Notations
• Chapter 1 Introduction
• Chapter 2 Review of Linear Algebra
• Chapter 3 Review of Statistical Results
• Chapter 4 Estimation in the Linear Model
• Chapter 5 Further Inference in the Linear Model
• Chapter 6 Analysis of Variance in Basic Designs
• Chapter 7 General Linear Model
• Chapter 8 Misspecified or Unknown Dispersion
• Chapter 9 Updates in the General Linear Model
• Chapter 10 Multivariate Linear Model
• Chapter 11 Linear Inference — Other Perspectives
• Solutions to Odd-Numbered Exercises
• Bibliography and Author Index
• Index