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


  • 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$68 / £46

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