LINEAR MODELS: An Integrated Approach

LINEAR MODELS
An Integrated Approach

by Debasis Sengupta (Indian Statistical Institute, Kolkata)
& S Rao Jammalamadaka (University of California, Santa Barbara)

Linear Models: An Integrated Approach aims to provide a clearer as well as a deeper unstanding of the general linear model using simple statistical f 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 statistical interpretation of complex algebraic results
	A thorough treatment of the singular linear model, including the case of multivariate response
	A unified discussion of models with a partially unknown dispersion matrix, including mixed-effects / variance components models and models for spatial and time series data
	Insight into updates in the linear model and their connection with diagnostics, design, variable selection, the Kalman filter, etc.
	An extensive discussion of 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.

644pp	Pub. date: Mar 2003
ISBN 981-02-4592-0	US$82 / £60

Reviews:

Mathematical Reviews (MR 1993512)
Zentralblatt MATH (Zbl 1049.62080)
Sankhya (Vol. 67, Pt. 1, Year 2005, pp.150)
Monatshefte fur Mathematik (Vol. 143 No. 3 Year 2004)

Look inside the book at amazon.com.

Material related to the book:

Errata
Data sets
Solutions to Exercises (PDF document, 50 pages, 510 KB) :
Available to teachers, password needed, you will need Adobe Acrobat reader to access it. If you do not have a password, mail to Debasis Sengupta to receive it.

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