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Linear Models for Multivariate, Time Series, and Spatial Data Ronald Christensen

Linear Models for Multivariate, Time Series, and Spatial Data

Ronald Christensen

Published August 15th 1997
ISBN :
Hardcover
336 pages
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 About the Book 

This is a self-contained companion volume to the authors book Plane Answers to Complex Questions: The Theory of Linear Models. It provides introductions to several topics related to linear model theory: multivariate linear models, discriminant analysis, principal components, factor analysis, time series in both the frequency and time domains, and spatial data analysis (geostatistics). The purpose of this volume is to use three fundamental ideas from linear model theory and exploit their properties in examining multivariate, time series and spatial data. The three ideas are: best linear prediction, projections, and Mahalanobis distance. Multivariate linear models are viewed as linear models with a nondiagonal covariance matrix. Discriminant analysis is related to the Mahalanobis distance and multivariate analysis of variance. Principle components are best linear predictors. Frequency domain time series involves linear models with a peculiar design matrix. Time domain analysis involves models that are linear in the parameters but have random design matrices. Best linear predictors are used for forecasting time series and for estimation in time domain analysis. Spatial data analysis involves linear models in which the covariance matrix is modeled from the data and making best linear unbiased predictions of future observables. This book develops a unified approach to this wide ranging collection of problems. Ronald Christensen is Professor of Statistics at the University of New Mexico. He is recognized internationally as an expert in the theory and application of linear models. In addition to this book and Plane Answers, he is the author of numerous research articles, Log-LinearModels and Logistic Regression, and Analysis of Variance, Design,