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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:
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Use
of simple statistical ideas such as linear zero functions and covariance
adjustment to explain the fundamental as well as advanced concepts |
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Emphasis
on statistical interpretation of complex algebraic results |
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A
thorough treatment of the singular linear model, including the case
of multivariate response |
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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 |
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Insight
into updates in the linear model and their connection with diagnostics,
design, variable selection, the Kalman filter, etc. |
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An
extensive discussion of the foundations of linear inference, along
with linear alternatives to least squares |
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Coverage
of other special topics such as collinearity, stochastic and inequality
constraints, misspecified models, etc. |
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Simpler
proofs of numerous known results |
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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$68 / £46 |
Material related to the book:
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