Linear regression:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2003
|
| Schriftenreihe: | Lecture notes in statistics
175 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 394 S. graph. Darst. |
| ISBN: | 3540401784 |
Internformat
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| 100 | 1 | |a Groß, Jürgen |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear regression |c Jürgen Groß |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a XII, 394 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in statistics |v 175 | |
| 650 | 4 | |a Analyse de régression | |
| 650 | 7 | |a Análise de regressão e de correlação |2 larpcal | |
| 650 | 7 | |a Análise multivariada |2 larpcal | |
| 650 | 7 | |a Lineaire regressie |2 gtt | |
| 650 | 7 | |a Regressieanalyse |2 gtt | |
| 650 | 4 | |a Regression analysis | |
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Datensatz im Suchindex
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| adam_text | TABLE OF CONTENTS PART I POINT ESTIMATION AND LINEAR REGRESSION 1
FUNDAMENTALS 3 1.1 LINEAR MODELS 3 1.1.1 APPLICATION OF LINEAR MODELS 3
1.1.2 TYPES OF LINEAR MODELS 6 1.1.3 PROCEEDING WITH LINEAR MODELS 7
1.1.4 A PRELIMINARY EXAMPLE 8 1.2 DECISION THEORY AND POINT ESTIMATION
12 1.2.1 DECISION RULE 12 1.2.2 NON-OPERATIONAL DECISION RULE 14 1.2.3
LOSS AND RISK 15 1.2.4 CHOOSING A DECISION RULE 16 1.2.5 ADMISSIBILITY
18 1.2.6 SQUARED ERROR LOSS 20 1.2.7 MATRIX VALUED SQUARED ERROR LOSS 22
1.2.8 ALTERNATIVE LOSS FUNCTIONS 26 1.3 PROBLEMS 29 2 THE LINEAR
REGRESSION MODEL 33 2.1 ASSUMPTIONS 33 2.2 ORDINARY LEAST SQUARES
ESTIMATION 36 2.2.1 THE PRINCIPLE OF LEAST SQUARES 37 2.2.2 COEFFICIENT
OF DETERMINATION R 2 39 2.2.3 PREDICTIVE LOSS 41 2.2.4 LEAST SQUARES
VARIANCE ESTIMATOR 44 2.2.5 PROPERTIES OF THE ORDINARY LEAST SQUARES
ESTIMATOR . . 45 2.2.6 PROPERTIES UNDER NORMALITY 46 2.3 OPTIMALITY OF
LEAST SQUARES ESTIMATION 47 2.3.1 LINEAR UNBIASED ESTIMATION 48 2.3.2
GAUSS-MARKOV THEOREM 49 2.3.3 NORMALITY ASSUMPTION 51 2.3.4
ADMISSIBILITY 52 2.4 UNRELIABILITY OF LEAST SQUARES ESTIMATION 53 2.4.1
ESTIMATION OF THE COVARIANCE MATRIX 53 VIII TABLE OF CONTENTS 2.4.2
UNBIASED VERSUS BIASED ESTIMATION 55 2.4.3 COLLINEARITY 57 2.4.4
CONSISTENCY 65 2.4.5 BIASED ESTIMATION 67 2.5 INADMISSIBILITY OF THE
ORDINARY LEAST SQUARES ESTIMATOR 69 2.5.1 THE REPARAMETERIZED REGRESSION
MODEL 69 2.5.2 RISK COMPARISON OF LEAST SQUARES AND STEIN ESTIMATOR 71
2.5.3 AN EXAMPLE FOR STEIN ESTIMATION 77 2.5.4 ADMISSIBILITY 78 2.6
PROBLEMS 80 PART II ALTERNATIVES TO LEAST SQUARES ESTIMATION 3
ALTERNATIVE ESTIMATORS 89 3.1 RESTRICTED LEAST SQUARES ESTIMATION 89
3.1.1 THE PRINCIPLE OF RESTRICTED LEAST SQUARES 90 3.1.2 THE PARAMETER
SPACE 91 3.1.3 PROPERTIES OF RESTRICTED LEAST SQUARES ESTIMATOR 92 3.1.4
RISK COMPARISON OF RESTRICTED AND ORDINARY LEAST SQUARES ESTIMATOR 94
3.1.5 PRETEST ESTIMATION 98 3.2 OTHER TYPES OF RESTRICTION 102 3.2.1
STOCHASTIC LINEAR RESTRICTIONS 102 3.2.2 INEQUALITY RESTRICTIONS 103
3.2.3 ELLIPTICAL RESTRICTIONS 105 3.3 PRINCIPAL COMPONENTS ESTIMATOR 106
3.3.1 PRELIMINARY CONSIDERATIONS 107 3.3.2 PROPERTIES OF THE PRINCIPAL
COMPONENTS ESTIMATOR .... 108 3.3.3 DRAWBACKS OF THE PRINCIPAL
COMPONENTS ESTIMATOR . . . 113 3.3.4 THE MARQUARDT ESTIMATOR 114 3.4
RIDGE ESTIMATOR 115 3.4.1 PRELIMINARY CONSIDERATIONS 115 3.4.2
PROPERTIES OF THE LINEAR RIDGE ESTIMATOR 118 3.4.3 THE CHOICE OF THE
RIDGE PARAMETER 123 3.4.4 STANDARDIZATION 128 3.4.5 RIDGE AND RESTRICTED
LEAST SQUARES ESTIMATOR 134 3.4.6 RIDGE AND PRINCIPAL COMPONENTS
ESTIMATOR 138 3.4.7 JACKKNIFE MODIFIED RIDGE ESTIMATOR 141 3.4.8
ITERATION ESTIMATOR 144 3.4.9 AN EXAMPLE FOR RIDGE ESTIMATION 147 3.5
SHRINKAGE ESTIMATOR 150 3.5.1 PRELIMINARY CONSIDERATIONS 150 3.5.2 RISK
COMPARISON TO ORDINARY LEAST SQUARES 152 3.5.3 THE CHOICE OF THE
SHRINKAGE PARAMETER 153 TABLE OF CONTENTS IX 3.5.4 DIRECTION MODIFIED
SHRINKAGE ESTIMATORS 157 3.6 GENERAL RIDGE ESTIMATOR 163 3.6.1 A CLASS
OF ESTIMATORS 163 3.6.2 RISK COMPARISON OF GENERAL RIDGE AND ORDINARY
LEAST SQUARES ESTIMATOR 164 3.7 LINEAR MINIMAX ESTIMATOR 165 3.7.1
PRELIMINARY CONSIDERATIONS 166 3.7.2 INEQUALITY RESTRICTIONS 167 3.7.3
LINEAR MINIMAX SOLUTIONS 169 3.7.4 ALTERNATIVE APPROACHES 174 3.7.5
ADMISSIBILITY 179 3.8 LINEAR BAYES ESTIMATOR 181 3.8.1 PRELIMINARY
CONSIDERATIONS 181 3.8.2 CHARACTERIZATION OF LINEAR BAYES ESTIMATORS 182
3.8.3 NON-OPERATIONAL BAYES SOLUTIONS 184 3.8.4 A-PRIORI ASSUMPTIONS 185
3.9 ROBUST ESTIMATOR 188 3.9.1 PRELIMINARY CONSIDERATIONS 189 3.9.2
WEIGHTED LEAST SQUARES ESTIMATION 192 3.9.3 THE H ESTIMATOR 197 3.9.4 M
ESTIMATOR 202 3.9.5 ROBUST RIDGE ESTIMATOR 203 3.10 PROBLEMS 204 LINEAR
ADMISSIBILITY 213 4.1 PRELIMINARY CONSIDERATIONS 213 4.2 LINEAR
ADMISSIBILITY IN THE NON-RESTRICTED MODEL 215 4.2.1 LINEAR ADMISSIBILITY
IN THE SIMPLE MEAN SHIFT MODEL . 215 4.2.2 CHARACTERIZATION OF LINEARLY
ADMISSIBLE ESTIMATORS .. . 219 4.2.3 ORDINARY LEAST SQUARES AND LINEARLY
ADMISSIBLE ESTIMATOR 222 4.2.4 LINEAR TRANSFORMS OF ORDINARY LEAST
SQUARES ESTIMATOR224 4.2.5 LINEAR ADMISSIBILITY OF KNOWN ESTIMATORS 226
4.2.6 SHRINKAGE PROPERTY AND LINEAR ADMISSIBILITY 229 4.2.7 CONVEX
COMBINATION OF ESTIMATORS 231 4.2.8 LINEAR BAYES ESTIMATOR 236 4.3
LINEAR ADMISSIBILITY UNDER LINEAR RESTRICTIONS 238 4.3.1 THE ASSUMPTION
OF A FULL RANK RESTRICTION MATRIX . . . 238 4.3.2 RESTRICTED ESTIMATOR
239 4.3.3 CHARACTERIZATION OF LINEARLY ADMISSIBLE ESTIMATORS .. . 244
4.4 LINEAR ADMISSIBILITY UNDER ELLIPTICAL RESTRICTIONS 246 4.4.1
CHARACTERIZATION OF LINEARLY ADMISSIBLE ESTIMATORS .. . 247 4.4.2 LINEAR
ADMISSIBILITY OF CERTAIN LINEAR ESTIMATORS .... 249 4.4.3 ADMISSIBLE
IMPROVEMENTS OVER ORDINARY LEAST SQUARES 251 4.5 PROBLEMS 254 X TABLE OF
CONTENTS PART III MISCELLANEOUS TOPICS THE COVARIANCE MATRIX OF THE
ERROR VECTOR 259 5.1 ESTIMATION OF THE ERROR VARIANCE 259 5.1.1 THE
SAMPLE VARIANCE 259 5.1.2 NONNEGATIVE UNBIASED ESTIMATION 260 5.1.3
OPTIMALITY OF THE LEAST SQUARES VARIANCE ESTIMATOR . . 261 5.1.4
NON-ADMISSIBILITY OF THE LEAST SQUARES VARIANCE ESTIMATOR 262 5.2
NON-SCALAR COVARIANCE MATRIX 265 5.2.1 PRELIMINARY CONSIDERATIONS 266
5.2.2 THE TRANSFORMED MODEL 267 5.2.3 TWO-STAGE ESTIMATION 270 5.3
OCCURRENCE OF NON-SCALAR COVARIANCE MATRICES 271 5.3.1 SEEMINGLY
UNRELATED REGRESSION 271 5.3.2 HETEROSCEDASTIC ERRORS 274 5.3.3
EQUICORRELATED ERRORS 280 5.3.4 AUTOCORRELATED ERRORS 281 5.4 SINGULAR
COVARIANCE MATRICES 284 5.5 EQUALITY OF ORDINARY AND GENERALIZED LEAST
SQUARES 287 5.6 PROBLEMS 289 REGRESSION DIAGNOSTICS 293 6.1 SELECTING
INDEPENDENT VARIABLES 293 6.1.1 MALLOWS C P 293 6.1.2 STEPWISE
REGRESSION 294 6.1.3 ALTERNATIVE CRITERIA 295 6.2 ASSESSING GOODNESS OF
FIT 298 6.3 DIAGNOSING COLLINEARITY 302 6.3.1 VARIANCE INFLATION FACTORS
302 6.3.2 SCALED CONDITION INDEXES 305 6.4 INSPECTING RESIDUALS 308
6.4.1 NORMAL QUANTILE PLOT 310 6.4.2 RESIDUALS VERSUS FITTED VALUES PLOT
310 6.4.3 FURTHER RESIDUAL PLOTS 312 6.5 FINDING INFLUENTIAL
OBSERVATIONS 313 6.5.1 LEVERAGE 313 6.5.2 INFLUENTIAL OBSERVATIONS 314
6.5.3 COLLINEARITY-INFLUENTIAL OBSERVATIONS 317 6.6 TESTING MODEL
ASSUMPTIONS 317 6.6.1 PRELIMINARY CONSIDERATIONS 317 6.6.2 TESTING FOR
HETEROSCEDASTICITY 318 6.6.3 TESTING FOR AUTOCORRELATION 320 6.6.4
TESTING FOR NON-NORMALITY 322 TABLE OF CONTENTS XI 6.6.5 TESTING FOR
NON-LINEARITY 323 6.6.6 TESTING FOR OUTLIER 326 6.7 PROBLEMS 327 A
MATRIX ALGEBRA 331 A.I PRELIMINARIES 331 A.1.1 MATRICES AND VECTORS 331
A.1.2 ELEMENTARY OPERATIONS 332 A.1.3 RANK OF A MATRIX 333 A.1.4
SUBSPACES AND MATRICES 334 A.1.5 PARTITIONED MATRICES 335 A.1.6
KRONECKER PRODUCT 336 A.1.7 MOORE-PENROSE INVERSE 337 A.2 COMMON
PITFALLS 338 A.3 SQUARE MATRICES 339 A.3.1 SPECIFIC SQUARE MATRICES 339
A.3.2 TRACE AND DETERMINANT 344 A.3.3 EIGENVALUE AND EIGENVECTOR 346
A.3.4 VECTOR AND MATRIX NORM 350 A.3.5 DEFINITENESS 351 A.4 SYMMETRIC
MATRIX 351 A.4.1 EIGENVALUES 351 A.4.2 SPECTRAL DECOMPOSITION 352 A.4.3
RAYLEIGH RATIO 353 A.4.4 DEFINITENESS 353 A.5 LOWNER PARTIAL ORDERING
356 B STOCHASTIC VECTORS 359 B.I EXPECTATION AND COVARIANCE 359 B.2
MULTIVARIATE NORMAL DISTRIBUTION 362 B.3 X 2 DISTRIBUTION 365 B.4 F
DISTRIBUTION 367 C AN EXAMPLE ANALYSIS WITH R 369 C.I PROBLEM AND GOAL
369 C.2 THE DATA 370 C.3 THE CHOICE OF VARIABLES 371 C.3.1 THE FULL
MODEL 371 C.3.2 STEPWISE REGRESSION 373 C.3.3 COLLINEARITY DIAGNOSTICS
374 C.4 FURTHER DIAGNOSTICS 375 C.4.1 RESIDUALS 375 C.4.2 INFLUENTIAL
OBSERVATIONS 377 C.5 PREDICTION 378 XII TABLE OF CONTENTS REFERENCES 381
INDEX 389
|
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| indexdate | 2024-07-09T19:14:26Z |
| institution | BVB |
| isbn | 3540401784 |
| language | English |
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| physical | XII, 394 S. graph. Darst. |
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| series2 | Lecture notes in statistics |
| spelling | Groß, Jürgen Verfasser aut Linear regression Jürgen Groß Berlin [u.a.] Springer 2003 XII, 394 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 175 Analyse de régression Análise de regressão e de correlação larpcal Análise multivariada larpcal Lineaire regressie gtt Regressieanalyse gtt Regression analysis Lineare Regression (DE-588)4167709-2 gnd rswk-swf Lineare Regression (DE-588)4167709-2 s DE-604 Lecture notes in statistics 175 (DE-604)BV002447846 175 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010344122&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Groß, Jürgen Linear regression Lecture notes in statistics Analyse de régression Análise de regressão e de correlação larpcal Análise multivariada larpcal Lineaire regressie gtt Regressieanalyse gtt Regression analysis Lineare Regression (DE-588)4167709-2 gnd |
| subject_GND | (DE-588)4167709-2 |
| title | Linear regression |
| title_auth | Linear regression |
| title_exact_search | Linear regression |
| title_full | Linear regression Jürgen Groß |
| title_fullStr | Linear regression Jürgen Groß |
| title_full_unstemmed | Linear regression Jürgen Groß |
| title_short | Linear regression |
| title_sort | linear regression |
| topic | Analyse de régression Análise de regressão e de correlação larpcal Análise multivariada larpcal Lineaire regressie gtt Regressieanalyse gtt Regression analysis Lineare Regression (DE-588)4167709-2 gnd |
| topic_facet | Analyse de régression Análise de regressão e de correlação Análise multivariada Lineaire regressie Regressieanalyse Regression analysis Lineare Regression |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010344122&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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