Advanced linear modeling: multivariate, time series, and spatial data ; nonparametric regression and response surface maximization
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| Previous Title: | Christensen, Ronald Linear models for multivariate, time series, and spatial data |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2001
|
| Edition: | 2. ed. |
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 377 - 389 |
| Physical Description: | XIII, 398 S. graph. Darst. |
| ISBN: | 0387952969 |
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| 100 | 1 | |a Christensen, Ronald |d 1951- |e Verfasser |0 (DE-588)111351820 |4 aut | |
| 245 | 1 | 0 | |a Advanced linear modeling |b multivariate, time series, and spatial data ; nonparametric regression and response surface maximization |c Ronald Christensen |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
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| 650 | 7 | |a Multivariate analyse |2 gtt | |
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Record in the Search Index
| _version_ | 1804128747653169152 |
|---|---|
| adam_text | Titel: Advanced linear modeling
Autor: Christensen, Ronald
Jahr: 2001
Contents
Preface to the Second Edition v
Preface to the First Edition vii
1 Multivariate Linear Models 1
1.1 Estimation ......................................................3
1.1.1 BLUEs ..................................................4
1.1.2 Maximum Likelihood Estimates........................5
1.1.3 Unbiased Estimation of £..............................8
1.2 Testing Hypotheses..............................................9
1.2.1 Test Statistics............................................12
1.2.2 Prediction Regions......................................21
1.2.3 Multiple Comparison Methods........................22
1.3 One-Sample Problems..........................................24
1.4 Two-Sample Problems..........................................30
1.5 One-Way Analysis of Variance and Profile Analysis..........33
1.5.1 Profile Analysis..........................................40
1.6 Growth Curves..................................................49
1.6.1 Longitudinal Data......................................61
1.7 Testing for Additional Information............................64
1.8 Additional Exercises............................................68
2 Discrimination and Allocation 74
2.1 The General Allocation Problem..............................76
Contents xi
2.1.1 Mahalanobis s Distance................ 76
2.1.2 Maximum Likelihood.................. 76
2.1.3 Bayesian Methods......................................77
2.1.4 Estimated Allocation....................................79
2.2 Equal Covariance Matrices......................................80
2.2.1 Cross-Validation........................................81
2.3 Linear Discrimination Coordinates............................94
2.4 Additional Exercises......................108
3 Principal Components and Factor Analysis 112
3.1 Properties of Best Linear Predictors.............113
3.2 The Theory of Principal Components.............119
3.2.1 Sequential Prediction .................119
3.2.2 Joint Prediction ....................121
3.2.3 Other Derivations of Principal Components.....123
3.2.4 Principal Components Based on the Correlation Matrixl26
3.3 Sample Principal Components.................126
3.3.1 The Sample Prediction Error.............128
3.3.2 Using Principal Components.............129
3.4 Factor Analysis.........................134
3.4.1 Terminology and Applications.............135
3.4.2 Maximum Likelihood Theory.............138
3.4.3 Principal Factor Estimation..............142
3.4.4 Discussion........................144
3.5 Additional Exercises......................148
4 Frequency Analysis of Time Series 152
4.1 Stationary Processes......................154
4.2 Basic Data Analysis......................155
4.3 Spectral Approximation of Stationary Time Series.....162
4.4 The Random Effects Model..................166
4.5 The Measurement Error Model................170
4.6 Linear Filtering.........................182
4.6.1 Recursive Filters....................186
4.7 The Coherence of Two Time Series..............188
4.8 Fourier Analysis ........................192
4.9 Additional Exercises......................194
5 Time Domain Analysis 200
5.1 Correlations...........................201
5.1.1 Partial Correlation and Best Linear Prediction . . . 203
5.2 Time Domain Models .....................204
5.2.1 Autoregressive Models: AR(pYs............204
5.2.2 Moving Average Models: MA(q)fs...........209
5.2.3 Autoregressive Moving Average Models: ARMA(p,qYs21Q
xii Contents
5.2.4 Autoregressive Integrated Moving Average Models:
ARIMA(p,d,qYs....................213
5.3 Time Domain Prediction....................213
5.4 Nonlinear Least Squares....................223
5.4.1 The Gauss-Newton Algorithm............224
5.4.2 Nonlinear Regression..................226
5.5 Estimation ...........................223
5.5.1 Correlations.......................228
5.5.2 Conditional Estimation for AR(p) Models......229
5.5.3 Conditional Least Squares for ARMA(p,qYs.....231
5.5.4 Conditional MLEs for ARMA(py q) s.........233
5.5.5 Unconditional Estimation for ARMA(p,q) Models . 235
5.5.6 Estimation for ARIMA(p, d, q) Models........239
5.6 Model Selection.........................239
5.6.1 Box-Jenkins ......................239
5.6.2 Model Selection Criteria................241
5.6.3 An Example ......................242
5.7 Seasonal Adjustment......................251
5.8 The Multivariate State-Space Model and the Kalman Filter 255
5.8.1 The Kalman Filter...................259
5.8.2 Parameter Estimation.................263
5.8.3 Missing Values.....................264
5.9 Additional Exercises......................265
6 Linear Models for Spatial Data: Kriging 269
6.1 Modeling Spatial Data.....................270
6.1.1 Stationarity.......................271
6.2 Best Linear Unbiased Prediction of Spatial Data: Kriging . 275
6.2.1 Block Kriging......................277
6.3 Prediction Based on the Semivariogram: Geostatistical Kriging278
6.4 Measurement Error and the Nugget Effect..........281
6.5 The Effect of Estimated Covariances on Prediction.....285
6.5.1 Spatial Data......................286
6.5.2 Mathematical Results.................287
6.6 Models for Covariance Functions and Semivariograms . . . 296
6.6.1 The Linear Covariance Model.............296
6.6.2 Nonlinear Isotropic Covariance Models........298
6.6.3 Modeling Anisotropic Covariance Functions.....299
6.6.4 Nonlinear Semivariograms...............299
6.7 Covariance Models for Lattice Data .............300
6.7.1 Spatial Covariance Selection Models.........300
6.7.2 Spatial Autoregression Models............301
6.7.3 Spatial Autoregressive Moving Average Models . . . 302
6.8 Estimation of Covariance Functions and Semivariograms . . 303
6.8.1 Estimation for Linear Covariance Functions.....304
Contents
xiu
6.8.2 Maximum Likelihood Estimation...........306
6.8.3 Residual Maximum Likelihood Estimation......308
6.8.4 Traditional Geostatistical Estimation.........309
7 Nonparametric Regression 312
7.1 Orthogonal Series Approximations..............314
7.2 Simple Nonparametric Regression...............316
7.3 Estimation ...........................317
7.4 Variable Selection........................328
7.5 Heteroscedastic Simple Nonparametric Regression .....332
7.6 Other Methods: Cubic Splines and Kernal Estimates .... 334
7.7 Nonparametric Multiple Regression..............337
7.8 Testing Lack of Fit.......................338
7.9 Other Methods: Regression Trees...............338
7.10 Density Estimation.......................341
7.11 Exercises ............................343
8 Response Surface Maximization 344
8.1 Approximating Response Functions..............346
8.2 First-Order Models and Steepest Ascent...........348
8.3 Fitting Quadratic Models...................359
8.4 Interpreting Quadratic Response Functions.........367
References 377
Author Index 390
Subject Index 393
|
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| author | Christensen, Ronald 1951- |
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| dewey-full | 519.5/3521 519.5/35 |
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| dewey-search | 519.5/35 21 519.5/35 |
| dewey-sort | 3519.5 235 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| isbn | 0387952969 |
| language | English |
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| spelling | Christensen, Ronald 1951- Verfasser (DE-588)111351820 aut Advanced linear modeling multivariate, time series, and spatial data ; nonparametric regression and response surface maximization Ronald Christensen 2. ed. New York [u.a.] Springer 2001 XIII, 398 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Literaturverz. S. 377 - 389 Lineaire modellen gtt Modelos lineares (pesquisa;planejamento) larpcal Modèles linéaires (Statistique) Multivariate analyse gtt Tijdreeksen gtt Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd rswk-swf Lineares Modell (DE-588)4134827-8 s DE-604 1. Auflage Christensen, Ronald Linear models for multivariate, time series, and spatial data HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Christensen, Ronald 1951- Advanced linear modeling multivariate, time series, and spatial data ; nonparametric regression and response surface maximization Lineaire modellen gtt Modelos lineares (pesquisa;planejamento) larpcal Modèles linéaires (Statistique) Multivariate analyse gtt Tijdreeksen gtt Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd |
| subject_GND | (DE-588)4134827-8 |
| title | Advanced linear modeling multivariate, time series, and spatial data ; nonparametric regression and response surface maximization |
| title_auth | Advanced linear modeling multivariate, time series, and spatial data ; nonparametric regression and response surface maximization |
| title_exact_search | Advanced linear modeling multivariate, time series, and spatial data ; nonparametric regression and response surface maximization |
| title_full | Advanced linear modeling multivariate, time series, and spatial data ; nonparametric regression and response surface maximization Ronald Christensen |
| title_fullStr | Advanced linear modeling multivariate, time series, and spatial data ; nonparametric regression and response surface maximization Ronald Christensen |
| title_full_unstemmed | Advanced linear modeling multivariate, time series, and spatial data ; nonparametric regression and response surface maximization Ronald Christensen |
| title_old | Christensen, Ronald Linear models for multivariate, time series, and spatial data |
| title_short | Advanced linear modeling |
| title_sort | advanced linear modeling multivariate time series and spatial data nonparametric regression and response surface maximization |
| title_sub | multivariate, time series, and spatial data ; nonparametric regression and response surface maximization |
| topic | Lineaire modellen gtt Modelos lineares (pesquisa;planejamento) larpcal Modèles linéaires (Statistique) Multivariate analyse gtt Tijdreeksen gtt Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd |
| topic_facet | Lineaire modellen Modelos lineares (pesquisa;planejamento) Modèles linéaires (Statistique) Multivariate analyse Tijdreeksen Linear models (Statistics) Lineares Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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