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LINEAR MODELS
An Integrated Approach
by Debasis Sengupta (Indian Statistical Institute, India) & Sreenivasa Rao Jammalamadaka (University of California, Santa Barbara, USA)
Table of Contents (247k)
Preface (318k)
Chapter 1: Introduction (935k)
Chapter 1.1: The Linear Mode (132k)
Chapter 1.2: Why a Linear Model (99k)
Chapter 1.3: Description of the Linear Model and Notations (147k)
Chapter 1.4: Scope of the Linear Model (194k)
Chapter 1.5: Related Models (141k)
Chapter 1.6: Uses of the Linear Model (165k)
Chapter 1.7: A Tour Through the Rest of the Book (218k)
Chapter 1.8: Exercises (230k)
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
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