Linear models and generalizations: least squares and alternatives
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Edition: | 3., extended ed. |
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Bis 2. Aufl. u.d.T.: Rao, Calyampudi Radhakrishna: Linear models |
| Physical Description: | XIX, 570 S. graph. Darst. |
| ISBN: | 9783540742265 3540742263 |
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| 245 | 1 | 0 | |a Linear models and generalizations |b least squares and alternatives |c C. Radhakrishna Rao ; Helge Toutenburg ... |
| 250 | |a 3., extended ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIX, 570 S. |b graph. Darst. | ||
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| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Bis 2. Aufl. u.d.T.: Rao, Calyampudi Radhakrishna: Linear models | ||
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| 650 | 7 | |a Pesquisa e planejamento estatístico |2 larpcal | |
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Record in the Search Index
| _version_ | 1804137210697482240 |
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| adam_text | C. RADHAKRISHNA RAO HELGE TOUTENBURG SHALABH CHRISTIAN HEUMANN LINEAR
MODELS AND GENERALIZATIONS LEAST SQUARES AND ALTERNATIVES THIRD EXTENDED
EDITION WITH CONTRIBUTIONS BY MICHAEL SCHOMAKER FYJ SPRINGER CONTENTS
PREFACE TO THE FIRST EDITION V PREFACE TO THE SECOND EDITION VII PREFACE
TO THE THIRD EDITION IX 1 INTRODUCTION 1 1.1 LINEAR MODELS AND
REGRESSION ANALYSIS 1 1.2 PLAN OF THE BOOK 3 2 THE SIMPLE LINEAR
REGRESSION MODEL 7 2.1 THE LINEAR MODEL 7 2.2 LEAST SQUARES ESTIMATION 8
2.3 DIRECT REGRESSION METHOD 10 2.4 PROPERTIES OF THE DIRECT REGRESSION
ESTIMATORS 12 2.5 CENTERED MODEL 14 2.6 NO INTERCEPT TERM MODEL 15 2.7
MAXIMUM LIKELIHOOD ESTIMATION 15 2.8 TESTING OF HYPOTHESES AND
CONFIDENCE INTERVAL ESTIMATION 17 2.9 ANALYSIS OF VARIANCE 20 2.10
GOODNESS OF FIT OF REGRESSION 23 2.11 REVERSE REGRESSION METHOD 24 2.12
ORTHOGONAL REGRESSION METHOD 24 2.13 REDUCED MAJOR AXIS REGRESSION
METHOD 27 XII CONTENTS 2.14 LEAST ABSOLUTE DEVIATION REGRESSION METHOD
29 2.15 ESTIMATION OF PARAMETERS WHEN X IS STOCHASTIC 30 3 THE MULTIPLE
LINEAR REGRESSION MODEL AND ITS EXTENSIONS 33 3.1 THE LINEAR MODEL 33
3.2 THE PRINCIPLE OF ORDINARY LEAST SQUARES (OLS) 35 3.3 GEOMETRIC
PROPERTIES OF OLS 36 3.4 BEST LINEAR UNBIASED ESTIMATION 38 3.4.1 BASIC
THEOREMS 38 3.4.2 LINEAR ESTIMATORS 43 3.4.3 MEAN DISPERSION ERROR 44
3.5 ESTIMATION (PREDICTION) OF THE ERROR TERM A AND A 2 . . . 45 3.6
CLASSICAL REGRESSION UNDER NORMAL ERRORS 46 3.6.1 THE MAXIMUM-LIKELIHOOD
(ML) PRINCIPLE .... 47 3.6.2 MAXIMUM LIKELIHOOD ESTIMATION IN CLASSICAL
NORMAL REGRESSION 47 3.7 CONSISTENCY OF ESTIMATORS 49 3.8 TESTING LINEAR
HYPOTHESES 51 3.9 ANALYSIS OF VARIANCE 57 3.10 GOODNESS OF FIT 59 3.11
CHECKING THE ADEQUACY OF REGRESSION ANALYSIS 61 3.11.1 UNIVARIATE
REGRESSION 61 3.11.2 MULTIPLE REGRESSION 61 3.11.3 A COMPLEX EXAMPLE 65
3.11.4 GRAPHICAL PRESENTATION 69 3.12 LINEAR REGRESSION WITH STOCHASTIC
REGRESSORS 70 3.12.1 REGRESSION AND MULTIPLE CORRELATION COEFFICIENT .
70 3.12.2 HETEROGENOUS LINEAR ESTIMATION WITHOUT NORMALITY 72 3.12.3
HETEROGENEOUS LINEAR ESTIMATION UNDER NORMALITY 73 3.13 THE CANONICAL
FORM 76 3.14 IDENTIFICATION AND QUANTIFICATION OF MULTICOLLINEARITY . .
77 3.14.1 PRINCIPAL COMPONENTS REGRESSION 77 3.14.2 RIDGE ESTIMATION 79
3.14.3 SHRINKAGE ESTIMATES 83 3.14.4 PARTIAL LEAST SQUARES 84 3.15 TESTS
OF PARAMETER CONSTANCY 87 3.15.1 THE CHOW FORECAST TEST 88 3.15.2 THE
HANSEN TEST 91 3.15.3 TESTS WITH RECURSIVE ESTIMATION 92 3.15.4 TEST FOR
STRUCTURAL CHANGE 93 3.16 TOTAL LEAST SQUARES 96 3.17 MINIMAX ESTIMATION
98 3.17.1 INEQUALITY RESTRICTIONS 98 CONTENTS XIII 3.17.2 THE MINIMAX
PRINCIPLE 101 3.18 CENSORED REGRESSION 105 3.18.1 OVERVIEW 105 3.18.2
LAD ESTIMATORS AND ASYMPTOTIC NORMALITY . . . 107 3.18.3 TESTS OF LINEAR
HYPOTHESES 108 3.19 SIMULTANEOUS CONFIDENCE INTERVALS 110 3.20
CONFIDENCE INTERVAL FOR THE RATIO OF TWO LINEAR PARAMETRIC FUNCTIONS 112
3.21 NONPARAMETRIC REGRESSION 112 3.21.1 ESTIMATION OF THE REGRESSION
FUNCTION 114 3.22 CLASSIFICATION AND REGRESSION TREES (CART) 117 3.23
BOOSTING AND BAGGING 121 3.24 PROJECTION PURSUIT REGRESSION 124 3.25
NEURAL NETWORKS AND NONPARAMETRIC REGRESSION 126 3.26 LOGISTIC
REGRESSION AND NEURAL NETWORKS 127 3.27 FUNCTIONAL DATA ANALYSIS (FDA)
127 3.28 RESTRICTED REGRESSION 130 3.28.1 PROBLEM OF SELECTION 130
3.28.2 THEORY OF RESTRICTED REGRESSION 130 3.28.3 EFFICIENCY OF
SELECTION 132 3.28.4 EXPLICIT SOLUTION IN SPECIAL CASES 133 3.29 LINEX
LOSS FUNCTION 135 3.30 BALANCED LOSS FUNCTION 137 3.31 COMPLEMENTS 138
3.31.1 LINEAR MODELS WITHOUT MOMENTS: EXERCISE .... 138 3.31.2 NONLINEAR
IMPROVEMENT OF OLSE FOR NONNORMAL DISTURBANCES 139 3.31.3 A
CHARACTERIZATION OF THE LEAST SQUARES ESTIMATOR 139 3.31.4 A
CHARACTERIZATION OF THE LEAST SQUARES ESTIMATOR: A LEMMA 140 3.32
EXERCISES 140 THE GENERALIZED LINEAR REGRESSION MODEL 143 4.1 OPTIMAL
LINEAR ESTIMATION OF FI 144 4.1.1 .FII-OPTIMAL ESTIMATORS 145 4.1.2 /?,
2 -OPTIMAL ESTIMATORS 149 4.1.3 IVOPTIMAL ESTIMATORS 150 4.2 THE AITKEN
ESTIMATOR 151 4.3 MISSPECIFICATION OF THE DISPERSION MATRIX 153 4.4
HETEROSCEDASTICITY AND AUTOREGRESSION 156 4.5 MIXED EFFECTS MODEL:
UNIFIED THEORY OF LINEAR ESTIMATION 164 4.5.1 MIXED EFFECTS MODEL 164
4.5.2 A BASIC LEMMA 164 4.5.3 ESTIMATION OF X/3 (THE FIXED EFFECT) 166
CONTENTS 4.5.4 PREDICTION OF U (THE RANDOM EFFECT) 166 4.5.5 ESTIMATION
OF E 167 4.6 LINEAR MIXED MODELS WITH NORMAL ERRORS AND R,ANDOM EFFECTS
168 4.6.1 MAXIMUM LIKELIHOOD ESTIMATION OF LINEAR MIXED MODELS 171 4.6.2
RESTRICTED MAXIMUM LIKELIHOOD ESTIMATION OF LINEAR MIXED MODELS 174
4.6.3 INFERENCE FOR LINEAR MIXED MODELS 178 4.7 REGRESSION-LIKE
EQUATIONS IN ECONOMETRICS 183 4.7.1 ECONOMETRIC MODELS 186 4.7.2 THE
R.EDUCED FORM 190 4.7.3 THE MULTIVARIATE REGRESSION MODEL 192 4.7.4 THE
CLASSICAL MULTIVARIATE LINEAR REGRESSION MODEL 195 4.7.5 STOCHASTIC
REGRESSION 196 4.7.6 INSTRUMENTAL VARIABLE ESTIMATOR 197 4.7.7 SEEMINGLY
UNRELATED REGRESSIONS 198 4.7.8 MEASUREMENT ERROR MODELS 199 4.8
SIMULTANEOUS PARAMETER ESTIMATION BY EMPIRICAL BAYES SOLUTIONS 209 4.8.1
OVERVIEW 209 4.8.2 ESTIMATION OF PARAMETERS FROM DIFFERENT LINEAR MODELS
211 4.9 SUPPLEMENTS 215 4.10 GAUSS-MARKOV, AITKEN AND R,AO LEAST SQUARES
ESTIMATORS 216 4.10.1 GAUSS-MARKOV LEAST SQUARES 216 4.10.2 AITKEN LEAST
SQUARES 217 4.10.3 RAO LEAST SQUARES 218 4.11 EXERCISES 220 EXACT AND
STOCHASTIC LINEAR RESTRICTIONS 223 5.1 USE OF PRIOR INFORMATION 223 5.2
THE RESTRICTED LEAST-SQUARES ESTIMATOR 225 5.3 MAXIMUM LIKELIHOOD
ESTIMATION UNDER EXACT RESTRICTIONS 227 5.4 STEPWISE INCLUSION OF EXACT
LINEAR RESTRICTIONS 228 5.5 BIASED LINEAR RESTRICTIONS AND MDE
COMPARISON WITH THE OLSE 233 5.6 MDE MATRIX COMPARISONS OF TWO BIASED
ESTIMATORS . . 236 5.7 MDE MATRIX COMPARISON OF TWO LINEAR BIASED
ESTIMATORS 242 5.8 MDE COMPARISON OF TWO (BIASED) RESTRICTED ESTIMATORS
243 5.9 STEIN-RULE ESTIMATORS UNDER EXACT RESTRICTIONS 251 5.10
STOCHASTIC LINEAR RESTRICTIONS 252 5.10.1 MIXED ESTIMATOR 252 5.10.2
ASSUMPTIONS ABOUT THE DISPERSION MATRIX .... 254 CONTENTS XV 5.10.3
BIASED STOCHASTIC RESTRICTIONS 257 5.11 STEIN-RULE ESTIMATORS UNDER
STOCHASTIC RESTRICTIONS . . . 261 5.12 WEAKENED LINEAR RESTRICTIONS 262
5.12.1 WEAKLY (R, R)-UNBIASEDNESS 262 5.12.2 OPTIMAL WEAKLY (R,
R)-UNBIASED ESTIMATORS . . . 262 5.12.3 FEASIBLE ESTIMATORS*OPTIMAL
SUBSTITUTION OF J3 IN PI(0,A) 266 5.12.4 RLSE INSTEAD OF THE MIXED
ESTIMATOR 268 5.13 EXERCISES 269 PREDICTION IN THE GENERALIZED
REGRESSION MODEL 271 6.1 INTRODUCTION 271 6.2 SOME SIMPLE LINEAR MODELS
271 6.2.1 THE CONSTANT MEAN MODEL 271 6.2.2 THE LINEAR TREND MODEL 272
6.2.3 POLYNOMIAL MODELS 273 6.3 THE PREDICTION MODEL . . . .- 274 6.4
OPTIMAL HETEROGENEOUS PREDICTION 275 6.5 OPTIMAL HOMOGENEOUS PREDICTION
277 6.6 MDE MATRIX COMPARISONS BETWEEN OPTIMAL AND CLASSICAL PREDICTORS
280 6.6.1 COMPARISON OF CLASSICAL AND OPTIMAL PREDICTION WITH RESPECT TO
THE Y* SUPERIORITY . . 283 6.6.2 COMPARISON OF CLASSICAL AND OPTIMAL
PREDICTORS WITH RESPECT TO THE X*/3 SUPERIORITY . 285 6.7 PREDICTION
REGIONS 287 6.7.1 CONCEPTS AND DEFINITIONS 287 6.7.2 ON G-PREDICTION
INTERVALS 289 6.7.3 ON ^-INTERVALS IN REGRESSION ANALYSIS 291 6.7.4 ON
(P, RY)-PREDICTION INTERVALS 292 6.7.5 LINEAR UTILITY FUNCTIONS 294
6.7.6 NORMALLY DISTRIBUTED POPULATIONS - TWO-SIDED SYMMETRIC INTERVALS
296 6.7.7 ONESIDED INFINITE INTERVALS 298 6.7.8 UTILITY AND LENGTH OF
INTERVALS 298 6.7.9 UTILITY AND COVERAGE 300 6.7.10 MAXIMAL UTILITY AND
OPTIMAL TESTS 300 6.7.11 PREDICTION ELLIPSOIDS BASED ON THE GLSE ....
302 6.7.12 COMPARING THE EFFICIENCY OF PREDICTION ELLIPSOIDS 305 6.8
SIMULTANEOUS PREDICTION OF ACTUAL AND AVERAGE VALUES OF Y 306 6.8.1
SPECIFICATION OF TARGET FUNCTION 307 6.8.2 EXACT LINEAR RESTRICTIONS 308
6.8.3 MDEP USING ORDINARY LEAST SQUARES ESTIMATOR 309 6.8.4 MDEP USING
RESTRICTED ESTIMATOR 309 6.8.5 MDEP MATRIX COMPARISON 310 XVI CONTENTS
6.8.6 STEIN-RULE PREDICTOR 310 6.8.7 OUTSIDE SAMPLE PREDICTIONS 311 6.9
KALMAN FILTER 314 6.9.1 DYNAMICAL AND OBSERVATIONAL EQUATIONS 314 6.9.2
SOME THEOREMS . . . 314 6.9.3 KALMAN MODEL 317 6.10 EXERCISES 318 7
SENSITIVITY ANALYSIS 321 7.1 INTRODUCTION 321 7.2 PREDICTION MATRIX 321
7.3 EFFECT OF SINGLE OBSERVATION ON ESTIMATION OF PARAMETERS 327 7.3.1
MEASURES BASED ON RESIDUALS 328 7.3.2 ALGEBRAIC CONSEQUENCES OF OMITTING
AN OBSERVATION 329 7.3.3 DETECTION OF OUTLIERS 330 7.4 DIAGNOSTIC PLOTS
FOR TESTING THE MODEL ASSUMPTIONS . . . 334 7.5 MEASURES BASED ON THE
CONFIDENCE ELLIPSOID 335 7.6 PARTIAL REGRESSION PLOTS 341 7.7 REGRESSION
DIAGNOSTICS FOR REMOVING AN OBSERVATION WITH GRAPHICS 343 7.8 MODEL
SELECTION CRITERIA 350 7.8.1 AKAIKES INFORMATION CRITERION 351 7.8.2
BAYESIAN INFORMATION CRITERION 353 7.8.3 MALLOWS C P 353 7.8.4 EXAMPLE
355 7.9 EXERCISES 356 8 ANALYSIS OF INCOMPLETE DATA SETS 357 8.1
STATISTICAL METHODS WITH MISSING DATA 358 8.1.1 COMPLETE CASE ANALYSIS
358 8.1.2 AVAILABLE CASE ANALYSIS 358 8.1.3 FILLING IN THE MISSING
VALUES 359 8.1.4 MODEL-BASED PROCEDURES 359 8.2 MISSING-DATA MECHANISMS
360 8.2.1 MISSING INDICATOR MATRIX 360 8.2.2 MISSING COMPLETELY AT
RANDOM 360 8.2.3 MISSING AT RANDOM 360 8.2.4 NONIGNORABLE NONRESPONSE
360 8.3 MISSING PATTERN 360 8.4 MISSING DATA IN THE RESPONSE 361 8.4.1
LEAST-SQUARES ANALYSIS FOR FILLED-UP DATA,*YATES PROCEDURE 362 8.4.2
ANALYSIS OF COVARIANCE*BARTLETT S METHOD . . . 363 8.5 SHRINKAGE
ESTIMATION BY YATES PROCEDURE 364 CONTENTS XVII 8.5.1 SHRINKAGE
ESTIMATORS 364 8.5.2 EFFICIENCY PROPERTIES 365 8.6 MISSING VALUES IN THE
X-MATRIX 367 8.6.1 GENERAL MODEL 367 8.6.2 MISSING VALUES AND LOSS IN
EFFICIENCY 368 8.7 METHODS FOR INCOMPLETE X-MATRICES 371 8.7.1
COMPLETE CASE ANALYSIS 371 8.7.2 AVAILABLE CASE ANALYSIS 371 8.7.3
MAXIMUM-LIKELIHOOD METHODS 372 8.8 IMPUTATION METHODS FOR INCOMPLETE
X-MATRICES 373 8.8.1 MAXIMUM-LIKELIHOOD ESTIMATES OF MISSING VALUES 373
8.8.2 ZERO-ORDER REGRESSION 374 8.8.3 FIRST-ORDER REGRESSION 375 8.8.4
MULTIPLE IMPUTATION 377 8.8.5 WEIGHTED MIXED REGRESSION 378 8.8.6 THE
TWO-STAGE WMRE 382 8.9 ASSUMPTIONS ABOUT THE MISSING MECHANISM 384 8.10
REGRESSION DIAGNOSTICS TO IDENTIFY NON-MCAR PROCESSES 384 8.10.1
COMPARISON OF THE MEANS 384 8.10.2 COMPARING THE VARIANCE-COVARIANCE
MATRICES . . 385 8.10.3 DIAGNOSTIC MEASURES FROM SENSITIVITY ANALYSIS .
385 8.10.4 DISTRIBUTION OF THE MEASURES AND TEST PROCEDURE 385 8.11
TREATMENT OF NONIGNORABLE NONRESPONSE 386 8.11.1 JOINT DISTRIBUTION OF
(X, Y) WITH MISSING VALUES ONLY IN Y 386 8.11.2 CONDITIONAL DISTRIBUTION
OF Y GIVEN X WITH MISSING VALUES ONLY IN Y 388 8.11.3 CONDITIONAL
DISTRIBUTION OF Y GIVEN X WITH MISSING VALUES ONLY IN X 389 8.11.4 OTHER
APPROACHES 390 8.12 FURTHER LITERATURE 391 8.13 EXERCISES 391 ROBUST
REGRESSION 393 9.1 OVERVIEW 393 9.2 LEAST ABSOLUTE DEVIATION ESTIMATORS
* UNIVARIATE CASE 394 9.3 M-ESTIMATES: UNIVARIATE CASE 398 9.4
ASYMPTOTIC DISTRIBUTIONS OF LAD ESTIMATORS 401 9.4.1 UNIVARIATE CASE 401
9.4.2 MULTIVARIATE CASE 402 9.5 GENERAL M-ESTIMATES 403 9.6 TESTS OF
SIGNIFICANCE 407 XVIII CONTENTS 10 MODELS FOR CATEGORICAL RESPONSE
VARIABLES 411 10.1 GENERALIZED LINEAR MODELS 411 10.1.1 EXTENSION OF THE
REGRESSION MODEL 411 10.1.2 STRUCTURE OF THE GENERALIZED LINEAR MODEL .
. . . 413 10.1.3 SCORE FUNCTION AND INFORMATION MATRIX .. ... 416 10.1.4
MAXIMUM-LIKELIHOOD ESTIMATION 417 10.1.5 TESTING OF HYPOTHESES AND
GOODNESS OF FIT . . . 420 10.1.6 OVERDISPERSION 421 10.1.7 QUASI
LOGLIKELIHOOD 423 10.2 CONTINGENCY TABLES 425 10.2.1 OVERVIEW 425 10.2.2
WAYS OF COMPARING PROPORTIONS 427 10.2.3 SAMPLING IN TWO-WAY CONTINGENCY
TABLES ... 429 10.2.4 LIKELIHOOD FUNCTION AND MAXIMUM-LIKELIHOOD
ESTIMATES 430 10.2.5 TESTING THE GOODNESS OF FIT 432 10.3 GLM FOR BINARY
RESPONSE 435 10.3.1 LOGIT MODELS AND LOGISTIC REGRESSION 435 10.3.2
TESTING THE MODEL 437 10.3.3 DISTRIBUTION FUNCTION AS A LINK FUNCTION
.... 438 10.4 LOGIT MODELS FOR CATEGORICAL DATA 439 10.5 GOODNESS OF
FIT*LIKELIHOOD-RATIO TEST 440 10.6 LOGLINEAR MODELS FOR CATEGORICAL
VARIABLES 441 10.6.1 TWO-WAY CONTINGENCY TABLES 441 10.6.2 THREE-WAY
CONTINGENCY TABLES 444 10.7 THE SPECIAL CASE OF BINARY RESPONSE 448 10.8
CODING OF CATEGORICAL EXPLANATORY VARIABLES 450 10.8.1 DUMMY AND EFFECT
CODING 450 10.8.2 CODING OF RESPONSE MODELS 453 10.8.3 CODING OF MODELS
FOR THE HAZARD RATE 455 10.9 EXTENSIONS TO DEPENDENT BINARY VARIABLES
457 10.9.1 OVERVIEW 458 10.9.2 MODELING APPROACHES FOR CORRELATED
RESPONSE . 460 10.9.3 QUASI-LIKELIHOOD APPROACH FOR CORRELATED BINARY
RESPONSE 460 10.9.4 THE GEE METHOD BY LIANG AND ZEGER 462 10.9.5
PROPERTIES OF THE GEE ESTIMATE J3 G 463 10.9.6 EFFICIENCY OF THE GEE AND
IEE METHODS 465 10.9.7 CHOICE OF THE QUASI-CORRELATION MATRIX R T (A) .
. 465 10.9.8 BIVARIATE BINARY CORRELATED RESPONSE VARIABLES 466 10.9.9
THE GEE METHOD 467 10.9.10 THE IEE METHOD 468 10.9.11 AN EXAMPLE FROM
THE FIELD OF DENTISTRY 469 10.9.12 FULL LIKELIHOOD APPROACH FOR MARGINAL
MODELS . 474 CONTENTS XIX 10.10 EXERCISES 486 A MATRIX ALGEBRA 489 A.I
OVERVIEW 489 A.2 TRACE OF A MATRIX 491 A.3 DETERMINANT OF A MATRIX 492
A.4 INVERSE OF A MATRIX 494 A.5 ORTHOGONAL MATRICES 495 A.6 RANK OF A
MATRIX 495 A.7 RANGE AND NULL SPACE 496 A.8 EIGENVALUES AND EIGENVECTORS
496 A.9 DECOMPOSITION OF MATRICES 498 A. 10 DEFINITE MATRICES AND
QUADRATIC FORMS 501 A. 11 IDEMPOTENT MATRICES 507 A.12 GENERALIZED
INVERSE 508 A.13 PROJECTORS 516 A. 14 FUNCTIONS OF NORMALLY DISTRIBUTED
VARIABLES 517 A. 15 DIFFERENTIATION OF SCALAR FUNCTIONS OF MATRICES 520
A. 16 MISCELLANEOUS R.ESULTS, STOCHASTIC CONVERGENCE 523 B TABLES 527 C
SOFTWARE FOR LINEAR REGRESSION MODELS 531 C.I SOFTWARE 531 C.2
SPECIAL-PURPOSE SOFTWARE 536 C.3 RESOURCES 537 REFERENCES 539 INDEX 563
|
| adam_txt |
C. RADHAKRISHNA RAO HELGE TOUTENBURG SHALABH CHRISTIAN HEUMANN LINEAR
MODELS AND GENERALIZATIONS LEAST SQUARES AND ALTERNATIVES THIRD EXTENDED
EDITION WITH CONTRIBUTIONS BY MICHAEL SCHOMAKER FYJ SPRINGER CONTENTS
PREFACE TO THE FIRST EDITION V PREFACE TO THE SECOND EDITION VII PREFACE
TO THE THIRD EDITION IX 1 INTRODUCTION 1 1.1 LINEAR MODELS AND
REGRESSION ANALYSIS 1 1.2 PLAN OF THE BOOK 3 2 THE SIMPLE LINEAR
REGRESSION MODEL 7 2.1 THE LINEAR MODEL 7 2.2 LEAST SQUARES ESTIMATION 8
2.3 DIRECT REGRESSION METHOD 10 2.4 PROPERTIES OF THE DIRECT REGRESSION
ESTIMATORS 12 2.5 CENTERED MODEL 14 2.6 NO INTERCEPT TERM MODEL 15 2.7
MAXIMUM LIKELIHOOD ESTIMATION 15 2.8 TESTING OF HYPOTHESES AND
CONFIDENCE INTERVAL ESTIMATION 17 2.9 ANALYSIS OF VARIANCE 20 2.10
GOODNESS OF FIT OF REGRESSION 23 2.11 REVERSE REGRESSION METHOD 24 2.12
ORTHOGONAL REGRESSION METHOD 24 2.13 REDUCED MAJOR AXIS REGRESSION
METHOD 27 XII CONTENTS 2.14 LEAST ABSOLUTE DEVIATION REGRESSION METHOD
29 2.15 ESTIMATION OF PARAMETERS WHEN X IS STOCHASTIC 30 3 THE MULTIPLE
LINEAR REGRESSION MODEL AND ITS EXTENSIONS 33 3.1 THE LINEAR MODEL 33
3.2 THE PRINCIPLE OF ORDINARY LEAST SQUARES (OLS) 35 3.3 GEOMETRIC
PROPERTIES OF OLS 36 3.4 BEST LINEAR UNBIASED ESTIMATION 38 3.4.1 BASIC
THEOREMS 38 3.4.2 LINEAR ESTIMATORS 43 3.4.3 MEAN DISPERSION ERROR 44
3.5 ESTIMATION (PREDICTION) OF THE ERROR TERM A AND A 2 . . . 45 3.6
CLASSICAL REGRESSION UNDER NORMAL ERRORS 46 3.6.1 THE MAXIMUM-LIKELIHOOD
(ML) PRINCIPLE . 47 3.6.2 MAXIMUM LIKELIHOOD ESTIMATION IN CLASSICAL
NORMAL REGRESSION 47 3.7 CONSISTENCY OF ESTIMATORS 49 3.8 TESTING LINEAR
HYPOTHESES 51 3.9 ANALYSIS OF VARIANCE 57 3.10 GOODNESS OF FIT 59 3.11
CHECKING THE ADEQUACY OF REGRESSION ANALYSIS 61 3.11.1 UNIVARIATE
REGRESSION 61 3.11.2 MULTIPLE REGRESSION 61 3.11.3 A COMPLEX EXAMPLE 65
3.11.4 GRAPHICAL PRESENTATION 69 3.12 LINEAR REGRESSION WITH STOCHASTIC
REGRESSORS 70 3.12.1 REGRESSION AND MULTIPLE CORRELATION COEFFICIENT .
70 3.12.2 HETEROGENOUS LINEAR ESTIMATION WITHOUT NORMALITY 72 3.12.3
HETEROGENEOUS LINEAR ESTIMATION UNDER NORMALITY 73 3.13 THE CANONICAL
FORM 76 3.14 IDENTIFICATION AND QUANTIFICATION OF MULTICOLLINEARITY . .
77 3.14.1 PRINCIPAL COMPONENTS REGRESSION 77 3.14.2 RIDGE ESTIMATION 79
3.14.3 SHRINKAGE ESTIMATES 83 3.14.4 PARTIAL LEAST SQUARES 84 3.15 TESTS
OF PARAMETER CONSTANCY 87 3.15.1 THE CHOW FORECAST TEST 88 3.15.2 THE
HANSEN TEST 91 3.15.3 TESTS WITH RECURSIVE ESTIMATION 92 3.15.4 TEST FOR
STRUCTURAL CHANGE 93 3.16 TOTAL LEAST SQUARES 96 3.17 MINIMAX ESTIMATION
98 3.17.1 INEQUALITY RESTRICTIONS 98 CONTENTS XIII 3.17.2 THE MINIMAX
PRINCIPLE 101 3.18 CENSORED REGRESSION 105 3.18.1 OVERVIEW 105 3.18.2
LAD ESTIMATORS AND ASYMPTOTIC NORMALITY . . . 107 3.18.3 TESTS OF LINEAR
HYPOTHESES 108 3.19 SIMULTANEOUS CONFIDENCE INTERVALS 110 3.20
CONFIDENCE INTERVAL FOR THE RATIO OF TWO LINEAR PARAMETRIC FUNCTIONS 112
3.21 NONPARAMETRIC REGRESSION 112 3.21.1 ESTIMATION OF THE REGRESSION
FUNCTION 114 3.22 CLASSIFICATION AND REGRESSION TREES (CART) 117 3.23
BOOSTING AND BAGGING 121 3.24 PROJECTION PURSUIT REGRESSION 124 3.25
NEURAL NETWORKS AND NONPARAMETRIC REGRESSION 126 3.26 LOGISTIC
REGRESSION AND NEURAL NETWORKS 127 3.27 FUNCTIONAL DATA ANALYSIS (FDA)
127 3.28 RESTRICTED REGRESSION 130 3.28.1 PROBLEM OF SELECTION 130
3.28.2 THEORY OF RESTRICTED REGRESSION 130 3.28.3 EFFICIENCY OF
SELECTION 132 3.28.4 EXPLICIT SOLUTION IN SPECIAL CASES 133 3.29 LINEX
LOSS FUNCTION 135 3.30 BALANCED LOSS FUNCTION 137 3.31 COMPLEMENTS 138
3.31.1 LINEAR MODELS WITHOUT MOMENTS: EXERCISE . 138 3.31.2 NONLINEAR
IMPROVEMENT OF OLSE FOR NONNORMAL DISTURBANCES 139 3.31.3 A
CHARACTERIZATION OF THE LEAST SQUARES ESTIMATOR 139 3.31.4 A
CHARACTERIZATION OF THE LEAST SQUARES ESTIMATOR: A LEMMA 140 3.32
EXERCISES 140 THE GENERALIZED LINEAR REGRESSION MODEL 143 4.1 OPTIMAL
LINEAR ESTIMATION OF FI 144 4.1.1 .FII-OPTIMAL ESTIMATORS 145 4.1.2 /?,
2 -OPTIMAL ESTIMATORS 149 4.1.3 IVOPTIMAL ESTIMATORS 150 4.2 THE AITKEN
ESTIMATOR 151 4.3 MISSPECIFICATION OF THE DISPERSION MATRIX 153 4.4
HETEROSCEDASTICITY AND AUTOREGRESSION 156 4.5 MIXED EFFECTS MODEL:
UNIFIED THEORY OF LINEAR ESTIMATION 164 4.5.1 MIXED EFFECTS MODEL 164
4.5.2 A BASIC LEMMA 164 4.5.3 ESTIMATION OF X/3 (THE FIXED EFFECT) 166 '
CONTENTS 4.5.4 PREDICTION OF U (THE RANDOM EFFECT) 166 4.5.5 ESTIMATION
OF E 167 4.6 LINEAR MIXED MODELS WITH NORMAL ERRORS AND R,ANDOM EFFECTS
168 4.6.1 MAXIMUM LIKELIHOOD ESTIMATION OF LINEAR MIXED MODELS 171 4.6.2
RESTRICTED MAXIMUM LIKELIHOOD ESTIMATION OF LINEAR MIXED MODELS 174
4.6.3 INFERENCE FOR LINEAR MIXED MODELS 178 4.7 REGRESSION-LIKE
EQUATIONS IN ECONOMETRICS 183 4.7.1 ECONOMETRIC MODELS 186 4.7.2 THE
R.EDUCED FORM 190 4.7.3 THE MULTIVARIATE REGRESSION MODEL 192 4.7.4 THE
CLASSICAL MULTIVARIATE LINEAR REGRESSION MODEL 195 4.7.5 STOCHASTIC
REGRESSION 196 4.7.6 INSTRUMENTAL VARIABLE ESTIMATOR 197 4.7.7 SEEMINGLY
UNRELATED REGRESSIONS 198 4.7.8 MEASUREMENT ERROR MODELS 199 4.8
SIMULTANEOUS PARAMETER ESTIMATION BY EMPIRICAL BAYES SOLUTIONS 209 4.8.1
OVERVIEW 209 4.8.2 ESTIMATION OF PARAMETERS FROM DIFFERENT LINEAR MODELS
211 4.9 SUPPLEMENTS 215 4.10 GAUSS-MARKOV, AITKEN AND R,AO LEAST SQUARES
ESTIMATORS 216 4.10.1 GAUSS-MARKOV LEAST SQUARES 216 4.10.2 AITKEN LEAST
SQUARES 217 4.10.3 RAO LEAST SQUARES 218 4.11 EXERCISES 220 EXACT AND
STOCHASTIC LINEAR RESTRICTIONS 223 5.1 USE OF PRIOR INFORMATION 223 5.2
THE RESTRICTED LEAST-SQUARES ESTIMATOR 225 5.3 MAXIMUM LIKELIHOOD
ESTIMATION UNDER EXACT RESTRICTIONS 227 5.4 STEPWISE INCLUSION OF EXACT
LINEAR RESTRICTIONS 228 5.5 BIASED LINEAR RESTRICTIONS AND MDE
COMPARISON WITH THE OLSE 233 5.6 MDE MATRIX COMPARISONS OF TWO BIASED
ESTIMATORS . . 236 5.7 MDE MATRIX COMPARISON OF TWO LINEAR BIASED
ESTIMATORS 242 5.8 MDE COMPARISON OF TWO (BIASED) RESTRICTED ESTIMATORS
243 5.9 STEIN-RULE ESTIMATORS UNDER EXACT RESTRICTIONS 251 5.10
STOCHASTIC LINEAR RESTRICTIONS 252 5.10.1 MIXED ESTIMATOR 252 5.10.2
ASSUMPTIONS ABOUT THE DISPERSION MATRIX . 254 CONTENTS XV 5.10.3
BIASED STOCHASTIC RESTRICTIONS 257 5.11 STEIN-RULE ESTIMATORS UNDER
STOCHASTIC RESTRICTIONS . . . 261 5.12 WEAKENED LINEAR RESTRICTIONS 262
5.12.1 WEAKLY (R, R)-UNBIASEDNESS 262 5.12.2 OPTIMAL WEAKLY (R,
R)-UNBIASED ESTIMATORS . . . '262 5.12.3 FEASIBLE ESTIMATORS*OPTIMAL
SUBSTITUTION OF J3 IN PI(0,A) 266 5.12.4 RLSE INSTEAD OF THE MIXED
ESTIMATOR 268 5.13 EXERCISES 269 PREDICTION IN THE GENERALIZED
REGRESSION MODEL 271 6.1 INTRODUCTION 271 6.2 SOME SIMPLE LINEAR MODELS
271 6.2.1 THE CONSTANT MEAN MODEL 271 6.2.2 THE LINEAR TREND MODEL 272
6.2.3 POLYNOMIAL MODELS 273 6.3 THE PREDICTION MODEL . . . .- 274 6.4
OPTIMAL HETEROGENEOUS PREDICTION 275 6.5 OPTIMAL HOMOGENEOUS PREDICTION
277 6.6 MDE MATRIX COMPARISONS BETWEEN OPTIMAL AND CLASSICAL PREDICTORS
280 6.6.1 COMPARISON OF CLASSICAL AND OPTIMAL PREDICTION WITH RESPECT TO
THE Y* SUPERIORITY . . 283 6.6.2 COMPARISON OF CLASSICAL AND OPTIMAL
PREDICTORS WITH RESPECT TO THE X*/3 SUPERIORITY . 285 6.7 PREDICTION
REGIONS 287 6.7.1 CONCEPTS AND DEFINITIONS 287 6.7.2 ON G-PREDICTION
INTERVALS 289 6.7.3 ON ^-INTERVALS IN REGRESSION ANALYSIS 291 6.7.4 ON
(P, RY)-PREDICTION INTERVALS 292 6.7.5 LINEAR UTILITY FUNCTIONS 294
6.7.6 NORMALLY DISTRIBUTED POPULATIONS - TWO-SIDED SYMMETRIC INTERVALS
296 6.7.7 ONESIDED INFINITE INTERVALS 298 6.7.8 UTILITY AND LENGTH OF
INTERVALS 298 6.7.9 UTILITY AND COVERAGE 300 6.7.10 MAXIMAL UTILITY AND
OPTIMAL TESTS 300 6.7.11 PREDICTION ELLIPSOIDS BASED ON THE GLSE .
302 6.7.12 COMPARING THE EFFICIENCY OF PREDICTION ELLIPSOIDS 305 6.8
SIMULTANEOUS PREDICTION OF ACTUAL AND AVERAGE VALUES OF Y 306 6.8.1
SPECIFICATION OF TARGET FUNCTION 307 6.8.2 EXACT LINEAR RESTRICTIONS 308
6.8.3 MDEP USING ORDINARY LEAST SQUARES ESTIMATOR 309 6.8.4 MDEP USING
RESTRICTED ESTIMATOR 309 6.8.5 MDEP MATRIX COMPARISON 310 XVI CONTENTS
6.8.6 STEIN-RULE PREDICTOR 310 6.8.7 OUTSIDE SAMPLE PREDICTIONS 311 6.9
KALMAN FILTER 314 6.9.1 DYNAMICAL AND OBSERVATIONAL EQUATIONS 314 6.9.2
SOME THEOREMS .' . . 314 6.9.3 KALMAN MODEL 317 6.10 EXERCISES 318 7
SENSITIVITY ANALYSIS 321 7.1 INTRODUCTION 321 7.2 PREDICTION MATRIX 321
7.3 EFFECT OF SINGLE OBSERVATION ON ESTIMATION OF PARAMETERS 327 7.3.1
MEASURES BASED ON RESIDUALS 328 7.3.2 ALGEBRAIC CONSEQUENCES OF OMITTING
AN OBSERVATION 329 7.3.3 DETECTION OF OUTLIERS 330 7.4 DIAGNOSTIC PLOTS
FOR TESTING THE MODEL ASSUMPTIONS . . . 334 7.5 MEASURES BASED ON THE
CONFIDENCE ELLIPSOID 335 7.6 PARTIAL REGRESSION PLOTS 341 7.7 REGRESSION
DIAGNOSTICS FOR REMOVING AN OBSERVATION WITH GRAPHICS 343 7.8 MODEL
SELECTION CRITERIA 350 7.8.1 AKAIKES INFORMATION CRITERION 351 7.8.2
BAYESIAN INFORMATION CRITERION 353 7.8.3 MALLOWS C P 353 7.8.4 EXAMPLE
355 7.9 EXERCISES 356 8 ANALYSIS OF INCOMPLETE DATA SETS 357 8.1
STATISTICAL METHODS WITH MISSING DATA 358 8.1.1 COMPLETE CASE ANALYSIS
358 8.1.2 AVAILABLE CASE ANALYSIS 358 8.1.3 FILLING IN THE MISSING
VALUES 359 8.1.4 MODEL-BASED PROCEDURES 359 8.2 MISSING-DATA MECHANISMS
360 8.2.1 MISSING INDICATOR MATRIX 360 8.2.2 MISSING COMPLETELY AT
RANDOM 360 8.2.3 MISSING AT RANDOM 360 8.2.4 NONIGNORABLE NONRESPONSE
360 8.3 MISSING PATTERN 360 8.4 MISSING DATA IN THE RESPONSE 361 8.4.1
LEAST-SQUARES ANALYSIS FOR FILLED-UP DATA,*YATES PROCEDURE 362 8.4.2
ANALYSIS OF COVARIANCE*BARTLETT'S METHOD . . . 363 8.5 SHRINKAGE
ESTIMATION BY YATES PROCEDURE 364 CONTENTS XVII 8.5.1 SHRINKAGE
ESTIMATORS 364 8.5.2 EFFICIENCY PROPERTIES 365 8.6 MISSING VALUES IN THE
X-MATRIX 367 8.6.1 GENERAL MODEL 367 8.6.2 MISSING VALUES AND LOSS IN
EFFICIENCY ' 368 8.7 METHODS FOR INCOMPLETE X-MATRICES 371 8.7.1
COMPLETE CASE ANALYSIS 371 8.7.2 AVAILABLE CASE ANALYSIS 371 8.7.3
MAXIMUM-LIKELIHOOD METHODS 372 8.8 IMPUTATION METHODS FOR INCOMPLETE
X-MATRICES 373 8.8.1 MAXIMUM-LIKELIHOOD ESTIMATES OF MISSING VALUES 373
8.8.2 ZERO-ORDER REGRESSION 374 8.8.3 FIRST-ORDER REGRESSION 375 8.8.4
MULTIPLE IMPUTATION 377 8.8.5 WEIGHTED MIXED REGRESSION 378 8.8.6 THE
TWO-STAGE WMRE 382 8.9 ASSUMPTIONS ABOUT THE MISSING MECHANISM 384 8.10
REGRESSION DIAGNOSTICS TO IDENTIFY NON-MCAR PROCESSES 384 8.10.1
COMPARISON OF THE MEANS 384 8.10.2 COMPARING THE VARIANCE-COVARIANCE
MATRICES . . 385 8.10.3 DIAGNOSTIC MEASURES FROM SENSITIVITY ANALYSIS .
385 8.10.4 DISTRIBUTION OF THE MEASURES AND TEST PROCEDURE 385 8.11
TREATMENT OF NONIGNORABLE NONRESPONSE 386 8.11.1 JOINT DISTRIBUTION OF
(X, Y) WITH MISSING VALUES ONLY IN Y 386 8.11.2 CONDITIONAL DISTRIBUTION
OF Y GIVEN X WITH MISSING VALUES ONLY IN Y 388 8.11.3 CONDITIONAL
DISTRIBUTION OF Y GIVEN X WITH MISSING VALUES ONLY IN X 389 8.11.4 OTHER
APPROACHES 390 8.12 FURTHER LITERATURE 391 8.13 EXERCISES 391 ROBUST
REGRESSION 393 9.1 OVERVIEW 393 9.2 LEAST ABSOLUTE DEVIATION ESTIMATORS
* UNIVARIATE CASE 394 9.3 M-ESTIMATES: UNIVARIATE CASE 398 9.4
ASYMPTOTIC DISTRIBUTIONS OF LAD ESTIMATORS 401 9.4.1 UNIVARIATE CASE 401
9.4.2 MULTIVARIATE CASE 402 9.5 GENERAL M-ESTIMATES 403 9.6 TESTS OF
SIGNIFICANCE 407 XVIII CONTENTS 10 MODELS FOR CATEGORICAL RESPONSE
VARIABLES 411 10.1 GENERALIZED LINEAR MODELS 411 10.1.1 EXTENSION OF THE
REGRESSION MODEL 411 10.1.2 STRUCTURE OF THE GENERALIZED LINEAR MODEL .
. . . 413 10.1.3 SCORE FUNCTION AND INFORMATION MATRIX .'. 416 10.1.4
MAXIMUM-LIKELIHOOD ESTIMATION 417 10.1.5 TESTING OF HYPOTHESES AND
GOODNESS OF FIT . . . 420 10.1.6 OVERDISPERSION 421 10.1.7 QUASI
LOGLIKELIHOOD 423 10.2 CONTINGENCY TABLES 425 10.2.1 OVERVIEW 425 10.2.2
WAYS OF COMPARING PROPORTIONS 427 10.2.3 SAMPLING IN TWO-WAY CONTINGENCY
TABLES . 429 10.2.4 LIKELIHOOD FUNCTION AND MAXIMUM-LIKELIHOOD
ESTIMATES 430 10.2.5 TESTING THE GOODNESS OF FIT 432 10.3 GLM FOR BINARY
RESPONSE 435 10.3.1 LOGIT MODELS AND LOGISTIC REGRESSION 435 10.3.2
TESTING THE MODEL 437 10.3.3 DISTRIBUTION FUNCTION AS A LINK FUNCTION
. 438 10.4 LOGIT MODELS FOR CATEGORICAL DATA 439 10.5 GOODNESS OF
FIT*LIKELIHOOD-RATIO TEST 440 10.6 LOGLINEAR MODELS FOR CATEGORICAL
VARIABLES 441 10.6.1 TWO-WAY CONTINGENCY TABLES 441 10.6.2 THREE-WAY
CONTINGENCY TABLES 444 10.7 THE SPECIAL CASE OF BINARY RESPONSE 448 10.8
CODING OF CATEGORICAL EXPLANATORY VARIABLES 450 10.8.1 DUMMY AND EFFECT
CODING 450 10.8.2 CODING OF RESPONSE MODELS 453 10.8.3 CODING OF MODELS
FOR THE HAZARD RATE 455 10.9 EXTENSIONS TO DEPENDENT BINARY VARIABLES
457 10.9.1 OVERVIEW 458 10.9.2 MODELING APPROACHES FOR CORRELATED
RESPONSE . 460 10.9.3 QUASI-LIKELIHOOD APPROACH FOR CORRELATED BINARY
RESPONSE 460 10.9.4 THE GEE METHOD BY LIANG AND ZEGER 462 10.9.5
PROPERTIES OF THE GEE ESTIMATE J3 G 463 10.9.6 EFFICIENCY OF THE GEE AND
IEE METHODS 465 10.9.7 CHOICE OF THE QUASI-CORRELATION MATRIX R T (A) .
. 465 10.9.8 BIVARIATE BINARY CORRELATED RESPONSE VARIABLES 466 10.9.9
THE GEE METHOD 467 10.9.10 THE IEE METHOD 468 10.9.11 AN EXAMPLE FROM
THE FIELD OF DENTISTRY 469 10.9.12 FULL LIKELIHOOD APPROACH FOR MARGINAL
MODELS . 474 CONTENTS XIX 10.10 EXERCISES 486 A MATRIX ALGEBRA 489 A.I
OVERVIEW 489 A.2 TRACE OF A MATRIX ' 491 A.3 DETERMINANT OF A MATRIX 492
A.4 INVERSE OF A MATRIX 494 A.5 ORTHOGONAL MATRICES 495 A.6 RANK OF A
MATRIX 495 A.7 RANGE AND NULL SPACE 496 A.8 EIGENVALUES AND EIGENVECTORS
496 A.9 DECOMPOSITION OF MATRICES 498 A. 10 DEFINITE MATRICES AND
QUADRATIC FORMS 501 A. 11 IDEMPOTENT MATRICES 507 A.12 GENERALIZED
INVERSE 508 A.13 PROJECTORS 516 A. 14 FUNCTIONS OF NORMALLY DISTRIBUTED
VARIABLES 517 A. 15 DIFFERENTIATION OF SCALAR FUNCTIONS OF MATRICES 520
A. 16 MISCELLANEOUS R.ESULTS, STOCHASTIC CONVERGENCE 523 B TABLES 527 C
SOFTWARE FOR LINEAR REGRESSION MODELS 531 C.I SOFTWARE 531 C.2
SPECIAL-PURPOSE SOFTWARE 536 C.3 RESOURCES 537 REFERENCES 539 INDEX 563 |
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| any_adam_object_boolean | 1 |
| author_GND | (DE-588)119285924 (DE-588)107164310 |
| building | Verbundindex |
| bvnumber | BV022962827 |
| callnumber-first | Q - Science |
| callnumber-label | QA279 |
| callnumber-raw | QA279 |
| callnumber-search | QA279 |
| callnumber-sort | QA 3279 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 234 SK 840 |
| classification_tum | MAT 620f |
| ctrlnum | (OCoLC)173807301 (DE-599)DNB985382821 |
| dewey-full | 519.5/36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/36 |
| dewey-search | 519.5/36 |
| dewey-sort | 3519.5 236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 3., extended ed. |
| format | Book |
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| id | DE-604.BV022962827 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:05:32Z |
| indexdate | 2024-07-09T21:08:41Z |
| institution | BVB |
| isbn | 9783540742265 3540742263 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016167176 |
| oclc_num | 173807301 |
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| owner_facet | DE-19 DE-BY-UBM DE-703 DE-11 DE-91G DE-BY-TUM DE-824 |
| physical | XIX, 570 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Linear models and generalizations least squares and alternatives C. Radhakrishna Rao ; Helge Toutenburg ... 3., extended ed. Berlin [u.a.] Springer 2008 XIX, 570 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Bis 2. Aufl. u.d.T.: Rao, Calyampudi Radhakrishna: Linear models Modelos lineares larpcal Pesquisa e planejamento estatístico larpcal Linear models (Statistics) Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Lineares Modell (DE-588)4134827-8 gnd rswk-swf Wirtschaftstheorie (DE-588)4079351-5 gnd rswk-swf Lineares Modell (DE-588)4134827-8 s DE-604 Statistik (DE-588)4056995-0 s Lineare Optimierung (DE-588)4035816-1 s Wirtschaftstheorie (DE-588)4079351-5 s Rao, Calyampudi Radhakrishna 1920-2023 Sonstige (DE-588)119285924 oth Toutenburg, Helge 1943-2009 Sonstige (DE-588)107164310 oth HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016167176&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Linear models and generalizations least squares and alternatives Modelos lineares larpcal Pesquisa e planejamento estatístico larpcal Linear models (Statistics) Lineare Optimierung (DE-588)4035816-1 gnd Statistik (DE-588)4056995-0 gnd Lineares Modell (DE-588)4134827-8 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd |
| subject_GND | (DE-588)4035816-1 (DE-588)4056995-0 (DE-588)4134827-8 (DE-588)4079351-5 |
| title | Linear models and generalizations least squares and alternatives |
| title_auth | Linear models and generalizations least squares and alternatives |
| title_exact_search | Linear models and generalizations least squares and alternatives |
| title_exact_search_txtP | Linear models and generalizations least squares and alternatives |
| title_full | Linear models and generalizations least squares and alternatives C. Radhakrishna Rao ; Helge Toutenburg ... |
| title_fullStr | Linear models and generalizations least squares and alternatives C. Radhakrishna Rao ; Helge Toutenburg ... |
| title_full_unstemmed | Linear models and generalizations least squares and alternatives C. Radhakrishna Rao ; Helge Toutenburg ... |
| title_short | Linear models and generalizations |
| title_sort | linear models and generalizations least squares and alternatives |
| title_sub | least squares and alternatives |
| topic | Modelos lineares larpcal Pesquisa e planejamento estatístico larpcal Linear models (Statistics) Lineare Optimierung (DE-588)4035816-1 gnd Statistik (DE-588)4056995-0 gnd Lineares Modell (DE-588)4134827-8 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd |
| topic_facet | Modelos lineares Pesquisa e planejamento estatístico Linear models (Statistics) Lineare Optimierung Statistik Lineares Modell Wirtschaftstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016167176&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT raocalyampudiradhakrishna linearmodelsandgeneralizationsleastsquaresandalternatives AT toutenburghelge linearmodelsandgeneralizationsleastsquaresandalternatives |