Advanced Linear Modeling

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1 Ronald Christensen Advanced Linear Modeling Multivariate, Time Series, and Spatial Data; Nonparametric Regression and Response Surface Maximization Second Edition Springer

2 Preface to the Second Edition Preface to the First Edition v vii 1 Multivariate Linear Models Estimation BLUEs Maximum Likelihood Estimates Unbiased Estimation of S Testing Hypotheses Test Statistics Prediction Regions Multiple Comparison Methods One-Sample Problems Two-Sample Problems One-Way Analysis of Variance and Profile Analysis Profile Analysis Growth Curves.." Longitudinal Data Testing for Additional Information Additional Exercises 68 2 Discrimination and Allocation The General Allocation Problem 76

3 xi Mahalanobis's Distance Maximum Likelihood Bayesian Methods Estimated Allocation Equal Covariance Matrices Cross-Validation Linear Discrimination Coordinates Additional Exercises 108 Principal Components and Factor Analysis Properties of Best Linear Predictors The Theory of Principal Components Sequential Prediction Joint Prediction Other Derivations of Principal Components Principal Components Based on the Correlation Matrixl Sample Principal Components The Sample Prediction Error Using Principal Components Factor Analysis Terminology and Applications Maximum Likelihood Theory Principal Factor Estimation Discussion Additional Exercises 148 Frequency Analysis of Time Series Stationary Processes Basic Data Analysis Spectral Approximation of Stationary Time Series The Random Effects Model The Measurement Error Model Linear Filtering Recursive Filters The Coherence of Two Time Series Fourier Analysis Additional Exercises 194 Time Domain Analysis Correlations Partial Correlation and Best Linear Prediction Time Domain Models Autoregressive Models: AR(p)'s Moving Average Models: MA(q)'s Autoregressive Moving Average Models: ARMA(p,q)'s21Q

4 xii Contents Autoregressive Integrated Moving Average Models: ARIMA(p,d,q)'s Time Domain Prediction Nonlinear Least Squares The Gauss-Newton Algorithm Nonlinear Regression Estimation Correlations Conditional Estimation for AR{p) Models Conditional Least Squares for ARMA{p, q)'s Conditional MLEs for ARMA{p,qYs Unconditional Estimation for ARMA(p, q) Models Estimation for ARIMA{p,d,q) Models Model Selection Box-Jenkins Model Selection Criteria An Example Seasonal Adjustment The Multivariate State-Space Model and the Kalman Filter The Kalman Filter Parameter Estimation Missing Values Additional Exercises Linear Models for Spatial Data: Kriging Modeling Spatial Data Stationarity Best Linear Unbiased Prediction of Spatial Data: Kriging Block Kriging Prediction Based on the Semivariogram: Geostatistical Kriging Measurement Error and the Nugget Effect The Effect of Estimated Covariances on Prediction Spatial Data Mathematical Results Models for Covariance Functions and Semivariograms The Linear Covariance Model Nonlinear Isotropic Covariance Models Modeling Anisotropic Covariance Functions Nonlinear Semivariograms Covariance Models for Lattice Data Spatial Covariance Selection Models Spatial Autoregression Models Spatial Autoregressive Moving Average Models Estimation of Covariance Functions and Semivariograms Estimation for Linear Covariance Functions 304

5 xiii Maximum Likelihood Estimation Residual Maximum Likelihood Estimation Traditional Geostatistical Estimation Nonparametric Regression Orthogonal Series Approximations Simple Nonparametric Regression Estimation Variable Selection Heteroscedastic Simple Nonparametric Regression Other Methods: Cubic Splines and Kernal Estimates Nonparametric Multiple Regression Testing Lack of Fit Other Methods: Regression Trees Density Estimation Exercises Response Surface Maximization Approximating Response Functions First-Order Models and Steepest Ascent Fitting Quadratic Models Interpreting Quadratic Response Functions 367 References 377 Author Index 390 Subject Index 393

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