Linear regression analysis:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley-Interscience
2003
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| Edition: | 2. ed. |
| Series: | Wiley series in probability and statistics
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| Subjects: | |
| Online Access: | Publisher description Table of contents Table of contents Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 531 - 548 |
| Physical Description: | XVI, 557 S. graph. Darst. |
| ISBN: | 0471415405 |
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MARC
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| 100 | 1 | |a Seber, George A. F. |d 1938- |e Verfasser |0 (DE-588)124231934 |4 aut | |
| 245 | 1 | 0 | |a Linear regression analysis |c George A. F. Seber ; Alan J. Lee |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley-Interscience |c 2003 | |
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| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Literaturverz. S. 531 - 548 | ||
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| 700 | 1 | |a Lee, Alan J. |d 1946- |e Verfasser |0 (DE-588)128681977 |4 aut | |
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| _version_ | 1804138172773302272 |
|---|---|
| adam_text | Contents
Preface xv
1 Vectors of Random Variables 1
1.1 Notation 1
1.2 Statistical Models 2
1.3 Linear Regression Models 4
1.4 Expectation and Covariance Operators 5
Exercises la 8
1.5 Mean and Variance of Quadratic Forms 9
Exercises lb 12
1.6 Moment Generating Functions and Independence 13
Exercises lc 15
Miscellaneous Exercises 1 15
2 Multivariate Normal Distribution 17
2.1 Density Function 17
Exercises 2a 19
2.2 Moment Generating Functions 20
Exercises 2b 23
2.3 Statistical Independence 24
v
vi CONTENTS
Exercises 2c 26
2.4 Distribution of Quadratic Forms 27
Exercises 2d 31
Miscellaneous Exercises 2 31
3 Linear Regression: Estimation and Distribution Theory 35
3.1 Least Squares Estimation 35
Exercises 3a 41
3.2 Properties of Least Squares Estimates 42
Exercises 3b 44
3.3 Unbiased Estimation of a2 44
Exercises 3c 47
3.4 Distribution Theory 47
Exercises 3d 49
3.5 Maximum Likelihood Estimation 49
3.6 Orthogonal Columns in the Regression Matrix 51
Exercises 3e 52
3.7 Introducing Further Explanatory Variables 54
3.7.1 General Theory 54
3.7.2 One Extra Variable 57
Exercises 3f 58
3.8 Estimation with Linear Restrictions 59
3.8.1 Method of Lagrange Multipliers 60
3.8.2 Method of Orthogonal Projections 61
Exercises 3g 62
3.9 Design Matrix of Less Than Full Rank 62
3.9.1 Least Squares Estimation 62
Exercises 3h 64
3.9.2 Estimable Functions 64
Exercises 3i 65
3.9.3 Introducing Further Explanatory Variables 65
3.9.4 Introducing Linear Restrictions 65
Exercises 3j 66
3.10 Generalized Least Squares 66
Exercises 3k 69
3.11 Centering and Scaling the Explanatory Variables 69
3.11.1 Centering 70
3.11.2 Scaling 71
1
CONTENTS vii
Exercises 31 72
3.12 Bayesian Estimation 73
Exercises 3m 76
3.13 Robust Regression 77
3.13.1 M-Estimates 78
3.13.2 Estimates Based on Robust Location and Scale
Measures 80
3.13.3 Measuring Robustness 82
3.13.4 Other Robust Estimates 88
Exercises 3n 93
Miscellaneous Exercises 3 93
4 Hypothesis Testing 97
4.1 Introduction 97
4.2 Likelihood Ratio Test 98
4.3 F-Test 99
4.3.1 Motivation 99
4.3.2 Derivation 99
Exercises 4a 102
4.3.3 Some Examples 103
4.3.4 The Straight Line 107
Exercises 4b 109
4.4 Multiple Correlation Coefficient 110
Exercises 4c 113
4.5 Canonical Form for H 113
Exercises 4d 114
4.6 Goodness-of-Fit Test 115
4.7 F-Test and Projection Matrices 116
Miscellaneous Exercises 4 117
5 Confidence Intervals and Regions 119
5.1 Simultaneous Interval Estimation 119
5.1.1 Simultaneous Inferences 119
5.1.2 Comparison of Methods 124
5.1.3 Confidence Regions 125
5.1.4 Hypothesis Testing and Confidence Intervals 127
5.2 Confidence Bands for the Regression Surface 129
5.2.1 Confidence Intervals 129
5.2.2 Confidence Bands 129
viii CONTENTS
5.3 Prediction Intervals and Bands for the Response 131
5.3.1 Prediction Intervals 131
5.3.2 Simultaneous Prediction Bands 133
5.4 Enlarging the Regression Matrix 135
Miscellaneous Exercises 5 136
6 Straight-Line Regression 139
6.1 The Straight Line 139
6.1.1 Confidence Intervals for the Slope and Intercept 139
6.1.2 Confidence Interval for the a;-Intercept 140
6.1.3 Prediction Intervals and Bands 141
6.1.4 Prediction Intervals for the Response 145
6.1.5 Inverse Prediction (Calibration) 145
Exercises 6a 148
6.2 Straight Line through the Origin 149
6.3 Weighted Least Squares for the Straight Line 150
6.3.1 Known Weights 150
6.3.2 Unknown Weights 151
Exercises 6b 153
6.4 Comparing Straight Lines 154
6.4.1 General Model 154
6.4.2 Use of Dummy Explanatory Variables 156
Exercises 6c 157
6.5 Two-Phase Linear Regression 159
6.6 Local Linear Regression 162
Miscellaneous Exercises 6 163
7 Polynomial Regression 165
7.1 Polynomials in One Variable 165
7.1.1 Problem of Ill-Conditioning 165
7.1.2 Using Orthogonal Polynomials 166
7.1.3 Controlled Calibration 172
7.2 Piecewise Polynomial Fitting 172
7.2.1 Unsatisfactory Fit 172
7.2.2 Spline Functions 173
7.2.3 Smoothing Splines 176
7.3 Polynomial Regression in Several Variables 180
7.3.1 Response Surfaces 180
CONTENTS ix
7.3.2 Multidimensional Smoothing 184
Miscellaneous Exercises 7 185
8 Analysis of Variance 187
8.1 Introduction 187
8.2 One-Way Classification 188
8.2.1 General Theory 188
8.2.2 Confidence Intervals 192
8.2.3 Underlying Assumptions 195
Exercises 8a 196
8.3 Two-Way Classification (Unbalanced) 197
8.3.1 Representation as a Regression Model 197
8.3.2 Hypothesis Testing 197
8.3.3 Procedures for Testing the Hypotheses 201
8.3.4 Confidence Intervals 204
Exercises 8b 205
8.4 Two-Way Classification (Balanced) 206
Exercises 8c 209
8.5 Two-Way Classification (One Observation per Mean) 211
8.5.1 Underlying Assumptions 212
8.6 Higher-Way Classifications with Equal Numbers per Mean 216
8.6.1 Definition of Interactions 216
8.6.2 Hypothesis Testing 217
8.6.3 Missing Observations 220
Exercises 8d 221
8.7 Designs with Simple Block Structure 221
8.8 Analysis of Covariance 222
Exercises 8e 224
Miscellaneous Exercises 8 225
9 Departures from Underlying Assumptions 227
9.1 Introduction 227
9.2 Bias 228
9.2.1 Bias Due to Underfitting 228
9.2.2 Bias Due to Overfitting 230
Exercises 9a 231
9.3 Incorrect Variance Matrix 231
Exercises 9b 232
x CONTENTS
9.4 Effect of Outliers 233
9.5 Robustness of the F-Test to Nonnormality 235
9.5.1 Effect of the Regressor Variables 235
9.5.2 Quadratically Balanced F-Tests 236
Exercises 9c 239
9.6 Effect of Random Explanatory Variables 240
9.6.1 Random Explanatory Variables Measured without
Error 240
9.6.2 Fixed Explanatory Variables Measured with Error 241
9.6.3 Round-off Errors 245
9.6.4 Some Working Rules 245
9.6.5 Random Explanatory Variables Measured with Error 246
9.6.6 Controlled Variables Model 248
9.7 Collinearity 249
9.7.1 Effect on the Variances of the Estimated Coefficients 249
9.7.2 Variance Inflation Factors 254
9.7.3 Variances and Eigenvalues 255
9.7.4 Perturbation Theory 255
9.7.5 Collinearity and Prediction 261
Exercises 9d 261
Miscellaneous Exercises 9 262
10 Departures from Assumptions: Diagnosis and Remedies 265
10.1 Introduction 265
10.2 Residuals and Hat Matrix Diagonals 266
Exercises 10a 270
10.3 Dealing with Curvature 271
10.3.1 Visualizing Regression Surfaces 271
10.3.2 Transforming to Remove Curvature 275
10.3.3 Adding and Deleting Variables 277
Exercises 10b 279
10.4 Nonconstant Variance and Serial Correlation 281
10.4.1 Detecting Nonconstant Variance 281
10.4.2 Estimating Variance Functions 288
10.4.3 Transforming to Equalize Variances 291
10.4.4 Serial Correlation and the Durbin-Watson Test 292
Exercises 10c 294
10.5 Departures from Normality 295
10.5.1 Normal Plotting 295
CONTENTS xi
10.5.2 Transforming the Response 297
10.5.3 Transforming Both Sides 299
Exercises lOd 300
10.6 Detecting and Dealing with Outliers 301
10.6.1 Types of Outliers 301
10.6.2 Identifying High-Leverage Points 304
10.6.3 Leave-One-Out Case Diagnostics 306
10.6.4 Test for Outliers 310
10.6.5 Other Methods 311
Exercises lOe 314
10.7 Diagnosing Collinearity 315
10.7.1 Drawbacks of Centering 316
10.7.2 Detection of Points Influencing Collinearity 319
10.7.3 Remedies for Collinearity 320
Exercises lOf 326
Miscellaneous Exercises 10 327
11 Computational Algorithms for Fitting a Regression 329
11.1 Introduction 329
11.1.1 Basic Methods 329
11.2 Direct Solution of the Normal Equations 330
11.2.1 Calculation of the Matrix X X 330
11.2.2 Solving the Normal Equations 331
Exercises lla 337
11.3 QR Decomposition 338
11.3.1 Calculation of Regression Quantities 340
11.3.2 Algorithms for the QR and WU Decompositions 341
Exercises lib 352
11.4 Singular Value Decomposition 353
11.4.1 Regression Calculations Using the SVD 353
11.4.2 Computing the SVD 354
11.5 Weighted Least Squares 355
11.6 Adding and Deleting Cases and Variables 356
11.6.1 Updating Formulas 356
11.6.2 Connection with the Sweep Operator 357
11.6.3 Adding and Deleting Cases and Variables Using QR 360
11.7 Centering the Data 363
11.8 Comparing Methods 365
xii CONTENTS
11.8.1 Resources 365
11.8.2 Efficiency 366
11.8.3 Accuracy 369
11.8.4 Two Examples 372
11.8.5 Summary 373
Exercises lie 374
11.9 Rank-Deficient Case 376
11.9.1 Modifying the QR Decomposition 376
11.9.2 Solving the Least Squares Problem 378
11.9.3 Calculating Rank in the Presence of Round-off Error 378
11.9.4 Using the Singular Value Decomposition 379
11.10 Computing the Hat Matrix Diagonals 379
11.10.1 Using the Cholesky Factorization 380
11.10.2Using the Thin QR Decomposition 380
11.11 Calculating Test Statistics 380
11.12 Robust Regression Calculations 382
11.12.1 Algorithms for Li Regression 382
11.12.2 Algorithms for M- and GM-Estimation 384
11.12.3Elemental Regressions 385
11.12.4Algorithms for High-Breakdown Methods 385
Exercises lid 388
Miscellaneous Exercises 11 389
12 Prediction and Model Selection 391
12.1 Introduction 391
12.2 Why Select? 393
Exercises 12a 399
12.3 Choosing the Best Subset 399
12.3.1 Goodness-of-Fit Criteria 400
12.3.2 Criteria Based on Prediction Error 401
12.3.3 Estimating Distributional Discrepancies 407
12.3.4 Approximating Posterior Probabilities 410
Exercises 12b 413
12.4 Stepwise Methods 413
12.4.1 Forward Selection 414
12.4.2 Backward Elimination 416
12.4.3 Stepwise Regression 418
Exercises 12c 420
CONTENTS xiii
12.5 Shrinkage Methods 420
12.5.1 Stein Shrinkage 420
12.5.2 Ridge Regression 423
12.5.3 Garrote and Lasso Estimates 425
Exercises 12d 427
12.6 Bayesian Methods 428
12.6.1 Predictive Densities 428
12.6.2 Bayesian Prediction 431
12.6.3 Bayesian Model Averaging 433
Exercises 12e 433
12.7 Effect of Model Selection on Inference 434
12.7.1 Conditional and Unconditional Distributions 434
12.7.2 Bias 436
12.7.3 Conditional Means and Variances 437
12.7.4 Estimating Coefficients Using Conditional Likelihood 437
12.7.5 Other Effects of Model Selection 438
Exercises 12f 438
12.8 Computational Considerations 439
12.8.1 Methods for All Possible Subsets 439
12.8.2 Generating the Best Regressions 442
12.8.3 All Possible Regressions Using QR Decompositions 446
Exercises 12g 447
12.9 Comparison of Methods 447
12.9.1 Identifying the Correct Subset 447
12.9.2 Using Prediction Error as a Criterion 448
Exercises 12h 456
Miscellaneous Exercises 12 456
Appendix A Some Matrix Algebra 457
A.I Trace and Eigenvalues 457
A.2 Rank 458
A.3 Positive-Semidefinite Matrices 460
A.4 Positive-Definite Matrices 461
A.5 Permutation Matrices 464
A.6 Idempotent Matrices 464
A. 7 Eigenvalue Applications 465
A.8 Vector Differentiation 466
A.9 Patterned Matrices 466
xiv CONTENTS
A.10 Generalized Inverse 469
A.ll Some Useful Results 471
A.12 Singular Value Decomposition 471
A.13 Some Miscellaneous Statistical Results 472
A.14 Fisher Scoring 473
Appendix B Orthogonal Projections 475
B.I Orthogonal Decomposition of Vectors 475
B.2 Orthogonal Complements 477
B.3 Projections on Subspaces 477
Appendix C Tables 479
C.I Percentage Points of the Bonferroni ^-Statistic 480
C.2 Distribution of the Largest Absolute Value of k Student t
Variables 482
C.3 Working-Hotelling Confidence Bands for Finite Intervals 489
Outline Solutions to Selected Exercises 491
References 531
Index 549
|
| adam_txt |
Contents
Preface xv
1 Vectors of Random Variables 1
1.1 Notation 1
1.2 Statistical Models 2
1.3 Linear Regression Models 4
1.4 Expectation and Covariance Operators 5
Exercises la 8
1.5 Mean and Variance of Quadratic Forms 9
Exercises lb 12
1.6 Moment Generating Functions and Independence 13
Exercises lc 15
Miscellaneous Exercises 1 15
2 Multivariate Normal Distribution 17
2.1 Density Function 17
Exercises 2a 19
2.2 Moment Generating Functions 20
Exercises 2b 23
2.3 Statistical Independence 24
v
vi CONTENTS
Exercises 2c 26
2.4 Distribution of Quadratic Forms 27
Exercises 2d 31
Miscellaneous Exercises 2 31
3 Linear Regression: Estimation and Distribution Theory 35
3.1 Least Squares Estimation 35
Exercises 3a 41
3.2 Properties of Least Squares Estimates 42
Exercises 3b 44
3.3 Unbiased Estimation of a2 44
Exercises 3c 47
3.4 Distribution Theory 47
Exercises 3d 49
3.5 Maximum Likelihood Estimation 49
3.6 Orthogonal Columns in the Regression Matrix 51
Exercises 3e 52
3.7 Introducing Further Explanatory Variables 54
3.7.1 General Theory 54
3.7.2 One Extra Variable 57
Exercises 3f 58
3.8 Estimation with Linear Restrictions 59
3.8.1 Method of Lagrange Multipliers 60
3.8.2 Method of Orthogonal Projections 61
Exercises 3g 62
3.9 Design Matrix of Less Than Full Rank 62
3.9.1 Least Squares Estimation 62
Exercises 3h 64
3.9.2 Estimable Functions 64
Exercises 3i 65
3.9.3 Introducing Further Explanatory Variables 65
3.9.4 Introducing Linear Restrictions 65
Exercises 3j 66
3.10 Generalized Least Squares 66
Exercises 3k 69
3.11 Centering and Scaling the Explanatory Variables 69
3.11.1 Centering 70
3.11.2 Scaling 71
1
CONTENTS vii
Exercises 31 72
3.12 Bayesian Estimation 73
Exercises 3m 76
3.13 Robust Regression 77
3.13.1 M-Estimates 78
3.13.2 Estimates Based on Robust Location and Scale
Measures 80
3.13.3 Measuring Robustness 82
3.13.4 Other Robust Estimates 88
Exercises 3n 93
Miscellaneous Exercises 3 93
4 Hypothesis Testing 97
4.1 Introduction 97
4.2 Likelihood Ratio Test 98
4.3 F-Test 99
4.3.1 Motivation 99
4.3.2 Derivation 99
Exercises 4a 102
4.3.3 Some Examples 103
4.3.4 The Straight Line 107
Exercises 4b 109
4.4 Multiple Correlation Coefficient 110
Exercises 4c 113
4.5 Canonical Form for H 113
Exercises 4d 114
4.6 Goodness-of-Fit Test 115
4.7 F-Test and Projection Matrices 116
Miscellaneous Exercises 4 117
5 Confidence Intervals and Regions 119
5.1 Simultaneous Interval Estimation 119
5.1.1 Simultaneous Inferences 119
5.1.2 Comparison of Methods 124
5.1.3 Confidence Regions 125
5.1.4 Hypothesis Testing and Confidence Intervals 127
5.2 Confidence Bands for the Regression Surface 129
5.2.1 Confidence Intervals 129
5.2.2 Confidence Bands 129
viii CONTENTS
5.3 Prediction Intervals and Bands for the Response 131
5.3.1 Prediction Intervals 131
5.3.2 Simultaneous Prediction Bands 133
5.4 Enlarging the Regression Matrix 135
Miscellaneous Exercises 5 136
6 Straight-Line Regression 139
6.1 The Straight Line 139
6.1.1 Confidence Intervals for the Slope and Intercept 139
6.1.2 Confidence Interval for the a;-Intercept 140
6.1.3 Prediction Intervals and Bands 141
6.1.4 Prediction Intervals for the Response 145
6.1.5 Inverse Prediction (Calibration) 145
Exercises 6a 148
6.2 Straight Line through the Origin 149
6.3 Weighted Least Squares for the Straight Line 150
6.3.1 Known Weights 150
6.3.2 Unknown Weights 151
Exercises 6b 153
6.4 Comparing Straight Lines 154
6.4.1 General Model 154
6.4.2 Use of Dummy Explanatory Variables 156
Exercises 6c 157
6.5 Two-Phase Linear Regression 159
6.6 Local Linear Regression 162
Miscellaneous Exercises 6 163
7 Polynomial Regression 165
7.1 Polynomials in One Variable 165
7.1.1 Problem of Ill-Conditioning 165
7.1.2 Using Orthogonal Polynomials 166
7.1.3 Controlled Calibration 172
7.2 Piecewise Polynomial Fitting 172
7.2.1 Unsatisfactory Fit 172
7.2.2 Spline Functions 173
7.2.3 Smoothing Splines 176
7.3 Polynomial Regression in Several Variables 180
7.3.1 Response Surfaces 180
CONTENTS ix
7.3.2 Multidimensional Smoothing 184
Miscellaneous Exercises 7 185
8 Analysis of Variance 187
8.1 Introduction 187
8.2 One-Way Classification 188
8.2.1 General Theory 188
8.2.2 Confidence Intervals 192
8.2.3 Underlying Assumptions 195
Exercises 8a 196
8.3 Two-Way Classification (Unbalanced) 197
8.3.1 Representation as a Regression Model 197
8.3.2 Hypothesis Testing 197
8.3.3 Procedures for Testing the Hypotheses 201
8.3.4 Confidence Intervals 204
Exercises 8b 205
8.4 Two-Way Classification (Balanced) 206
Exercises 8c 209
8.5 Two-Way Classification (One Observation per Mean) 211
8.5.1 Underlying Assumptions 212
8.6 Higher-Way Classifications with Equal Numbers per Mean 216
8.6.1 Definition of Interactions 216
8.6.2 Hypothesis Testing 217
8.6.3 Missing Observations 220
Exercises 8d 221
8.7 Designs with Simple Block Structure 221
8.8 Analysis of Covariance 222
Exercises 8e 224
Miscellaneous Exercises 8 225
9 Departures from Underlying Assumptions 227
9.1 Introduction 227
9.2 Bias 228
9.2.1 Bias Due to Underfitting 228
9.2.2 Bias Due to Overfitting 230
Exercises 9a 231
9.3 Incorrect Variance Matrix 231
Exercises 9b 232
x CONTENTS
9.4 Effect of Outliers 233
9.5 Robustness of the F-Test to Nonnormality 235
9.5.1 Effect of the Regressor Variables 235
9.5.2 Quadratically Balanced F-Tests 236
Exercises 9c 239
9.6 Effect of Random Explanatory Variables 240
9.6.1 Random Explanatory Variables Measured without
Error 240
9.6.2 Fixed Explanatory Variables Measured with Error 241
9.6.3 Round-off Errors 245
9.6.4 Some Working Rules 245
9.6.5 Random Explanatory Variables Measured with Error 246
9.6.6 Controlled Variables Model 248
9.7 Collinearity 249
9.7.1 Effect on the Variances of the Estimated Coefficients 249
9.7.2 Variance Inflation Factors 254
9.7.3 Variances and Eigenvalues 255
9.7.4 Perturbation Theory 255
9.7.5 Collinearity and Prediction 261
Exercises 9d 261
Miscellaneous Exercises 9 262
10 Departures from Assumptions: Diagnosis and Remedies 265
10.1 Introduction 265
10.2 Residuals and Hat Matrix Diagonals 266
Exercises 10a 270
10.3 Dealing with Curvature 271
10.3.1 Visualizing Regression Surfaces 271
10.3.2 Transforming to Remove Curvature 275
10.3.3 Adding and Deleting Variables 277
Exercises 10b 279
10.4 Nonconstant Variance and Serial Correlation 281
10.4.1 Detecting Nonconstant Variance 281
10.4.2 Estimating Variance Functions 288
10.4.3 Transforming to Equalize Variances 291
10.4.4 Serial Correlation and the Durbin-Watson Test 292
Exercises 10c 294
10.5 Departures from Normality 295
10.5.1 Normal Plotting 295
CONTENTS xi
10.5.2 Transforming the Response 297
10.5.3 Transforming Both Sides 299
Exercises lOd 300
10.6 Detecting and Dealing with Outliers 301
10.6.1 Types of Outliers 301
10.6.2 Identifying High-Leverage Points 304
10.6.3 Leave-One-Out Case Diagnostics 306
10.6.4 Test for Outliers 310
10.6.5 Other Methods 311
Exercises lOe 314
10.7 Diagnosing Collinearity 315
10.7.1 Drawbacks of Centering 316
10.7.2 Detection of Points Influencing Collinearity 319
10.7.3 Remedies for Collinearity 320
Exercises lOf 326
Miscellaneous Exercises 10 327
11 Computational Algorithms for Fitting a Regression 329
11.1 Introduction 329
11.1.1 Basic Methods 329
11.2 Direct Solution of the Normal Equations 330
11.2.1 Calculation of the Matrix X'X 330
11.2.2 Solving the Normal Equations 331
Exercises lla 337
11.3 QR Decomposition 338
11.3.1 Calculation of Regression Quantities 340
11.3.2 Algorithms for the QR and WU Decompositions 341
Exercises lib 352
11.4 Singular Value Decomposition 353
11.4.1 Regression Calculations Using the SVD 353
11.4.2 Computing the SVD 354
11.5 Weighted Least Squares 355
11.6 Adding and Deleting Cases and Variables 356
11.6.1 Updating Formulas 356
11.6.2 Connection with the Sweep Operator 357
11.6.3 Adding and Deleting Cases and Variables Using QR 360
11.7 Centering the Data 363
11.8 Comparing Methods 365
xii CONTENTS
11.8.1 Resources 365
11.8.2 Efficiency 366
11.8.3 Accuracy 369
11.8.4 Two Examples 372
11.8.5 Summary 373
Exercises lie 374
11.9 Rank-Deficient Case 376
11.9.1 Modifying the QR Decomposition 376
11.9.2 Solving the Least Squares Problem 378
11.9.3 Calculating Rank in the Presence of Round-off Error 378
11.9.4 Using the Singular Value Decomposition 379
11.10 Computing the Hat Matrix Diagonals 379
11.10.1 Using the Cholesky Factorization 380
11.10.2Using the Thin QR Decomposition 380
11.11 Calculating Test Statistics 380
11.12 Robust Regression Calculations 382
11.12.1 Algorithms for Li Regression 382
11.12.2 Algorithms for M- and GM-Estimation 384
11.12.3Elemental Regressions 385
11.12.4Algorithms for High-Breakdown Methods 385
Exercises lid 388
Miscellaneous Exercises 11 389
12 Prediction and Model Selection 391
12.1 Introduction 391
12.2 Why Select? 393
Exercises 12a 399
12.3 Choosing the Best Subset 399
12.3.1 Goodness-of-Fit Criteria 400
12.3.2 Criteria Based on Prediction Error 401
12.3.3 Estimating Distributional Discrepancies 407
12.3.4 Approximating Posterior Probabilities 410
Exercises 12b 413
12.4 Stepwise Methods 413
12.4.1 Forward Selection 414
12.4.2 Backward Elimination 416
12.4.3 Stepwise Regression 418
Exercises 12c 420
CONTENTS xiii
12.5 Shrinkage Methods 420
12.5.1 Stein Shrinkage 420
12.5.2 Ridge Regression 423
12.5.3 Garrote and Lasso Estimates 425
Exercises 12d 427
12.6 Bayesian Methods 428
12.6.1 Predictive Densities 428
12.6.2 Bayesian Prediction 431
12.6.3 Bayesian Model Averaging 433
Exercises 12e 433
12.7 Effect of Model Selection on Inference 434
12.7.1 Conditional and Unconditional Distributions 434
12.7.2 Bias 436
12.7.3 Conditional Means and Variances 437
12.7.4 Estimating Coefficients Using Conditional Likelihood 437
12.7.5 Other Effects of Model Selection 438
Exercises 12f 438
12.8 Computational Considerations 439
12.8.1 Methods for All Possible Subsets 439
12.8.2 Generating the Best Regressions 442
12.8.3 All Possible Regressions Using QR Decompositions 446
Exercises 12g 447
12.9 Comparison of Methods 447
12.9.1 Identifying the Correct Subset 447
12.9.2 Using Prediction Error as a Criterion 448
Exercises 12h 456
Miscellaneous Exercises 12 456
Appendix A Some Matrix Algebra 457
A.I Trace and Eigenvalues 457
A.2 Rank 458
A.3 Positive-Semidefinite Matrices 460
A.4 Positive-Definite Matrices 461
A.5 Permutation Matrices 464
A.6 Idempotent Matrices 464
A. 7 Eigenvalue Applications 465
A.8 Vector Differentiation 466
A.9 Patterned Matrices 466
xiv CONTENTS
A.10 Generalized Inverse 469
A.ll Some Useful Results 471
A.12 Singular Value Decomposition 471
A.13 Some Miscellaneous Statistical Results 472
A.14 Fisher Scoring 473
Appendix B Orthogonal Projections 475
B.I Orthogonal Decomposition of Vectors 475
B.2 Orthogonal Complements 477
B.3 Projections on Subspaces 477
Appendix C Tables 479
C.I Percentage Points of the Bonferroni ^-Statistic 480
C.2 Distribution of the Largest Absolute Value of k Student t
Variables 482
C.3 Working-Hotelling Confidence Bands for Finite Intervals 489
Outline Solutions to Selected Exercises 491
References 531
Index 549 |
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| author | Seber, George A. F. 1938- Lee, Alan J. 1946- |
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| author_facet | Seber, George A. F. 1938- Lee, Alan J. 1946- |
| author_role | aut aut |
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| building | Verbundindex |
| bvnumber | BV023528252 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA278.2.S4 2003 |
| callnumber-search | QA278.2.S4 2003 |
| callnumber-sort | QA 3278.2 S4 42003 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 840 |
| ctrlnum | (OCoLC)249134962 (DE-599)BVBBV023528252 |
| dewey-full | 519.5/3621 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/36 21 |
| dewey-search | 519.5/36 21 |
| dewey-sort | 3519.5 236 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | Seber, George A. F. 1938- Verfasser (DE-588)124231934 aut Linear regression analysis George A. F. Seber ; Alan J. Lee 2. ed. Hoboken, NJ Wiley-Interscience 2003 XVI, 557 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Literaturverz. S. 531 - 548 Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Lineare Regression (DE-588)4167709-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Regressionsanalyse (DE-588)4129903-6 s DE-604 Lineare Regression (DE-588)4167709-2 s 2\p DE-604 Lee, Alan J. 1946- Verfasser (DE-588)128681977 aut http://www.loc.gov/catdir/description/wiley039/2003266044.html Publisher description http://www.loc.gov/catdir/toc/wiley032/2003266044.html Table of contents http://www.wiley.com/cda/product/0,,0471415405,00.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016848455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Seber, George A. F. 1938- Lee, Alan J. 1946- Linear regression analysis Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Lineare Regression (DE-588)4167709-2 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4167709-2 (DE-588)4151278-9 |
| title | Linear regression analysis |
| title_auth | Linear regression analysis |
| title_exact_search | Linear regression analysis |
| title_exact_search_txtP | Linear regression analysis |
| title_full | Linear regression analysis George A. F. Seber ; Alan J. Lee |
| title_fullStr | Linear regression analysis George A. F. Seber ; Alan J. Lee |
| title_full_unstemmed | Linear regression analysis George A. F. Seber ; Alan J. Lee |
| title_short | Linear regression analysis |
| title_sort | linear regression analysis |
| topic | Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Lineare Regression (DE-588)4167709-2 gnd |
| topic_facet | Regression analysis Regressionsanalyse Lineare Regression Einführung |
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