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
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.
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- ID: 9789810245924
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