Subset selection in regression:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton u.a.
Chapman & Hall / CRC
2002
|
| Edition: | 2. ed. |
| Series: | Monographs on statistics and applied probability
95 |
| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Physical Description: | XVII, 238 S. graph. Darst. |
| ISBN: | 1584881712 |
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MARC
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Record in the Search Index
| _version_ | 1804129139377045504 |
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| adam_text | Titel: Subset selection in regression
Autor: Miller, Alan J
Jahr: 2002
Contents
Preface to first edition ix
Preface to second edition xiii
1 Objectives
1.1 Prediction, explanation, elimination or what? 1
1.2 How many variables in the prediction formula? 3
1.3 Alternatives to using subsets 6
1.4 Black box use of best-subsets techniques 8
2 Least-squares computations
2.1 Using sums of squares and products matrices 11
2.2 Orthogonal reduction methods 16
2.3 Gauss-Jordan v. orthogonal reduction methods 20
2.4 Interpretation of projections 27
Appendix A. Operation counts for all-subsets regression 29
A.l Garside s Gauss-Jordan algorithm 30
A.2 Planar rotations and a Hamiltonian cycle 31
A.3 Planar rotations and a binary sequence 32
A.4 Fast planar rotations 34
3 Finding subsets which fit well
3.1 Objectives and limitations of this chapter 37
3.2 Forward selection 39
3.3 Efroymson s algorithm 42
3.4 Backward elimination 44
3.5 Sequential replacement algorithms 46
3.6 Replacing two variables at a time 48
3.7 Generating all subsets 48
3.8 Using branch-and-bound techniques 52
3.9 Grouping variables 54
3.10 Ridge regression and other alternatives 57
3.11 The nonnegative garrote and the lasso 60
3.12 Some examples 67
3.13 Conclusions and recommendations 84
Appendix A. An algorithm for the lasso 86
vii
viii
4 Hypothesis testing
4.1 Is there any information in the remaining variables? 89
4.2 Is one subset better than another? 97
4.2.1 Applications of Spj^tvoll s method 101
4.2.2 Using other confidence ellipsoids 104
Appendix A. Spj^tvoll s method - detailed description 106
5 When to stop?
5.1 What criterion should we use? HI
5.2 Prediction criteria 112
5.2.1 Mean squared errors of prediction (MSEP) 113
5.2.2 MSEP for the fixed model 114
5.2.3 MSEP for the random model 129
5.2.4 A simulation with random predictors 133
5.3 Cross-validation and the PRESS statistic 143
5.4 Bootstrapping 151
5.5 Likelihood and information-based stopping rules 154
5.5.1 Minimum description length (MDL) 158
Appendix A. Approximate equivalence of stopping rules 160
A.l F-to-enter 160
A.2 Adjusted R2 or Fisher s A-statistic 161
A.3 Akaike s information criterion (AIC) 162
6 Estimation of regression coefficients
6.1 Selection bias 165
6.2 Choice between two variables 166
6.3 Selection bias in the general case and its reduction 175
6.3.1 Monte Carlo estimation of bias in forward selection 178
6.3.2 Shrinkage methods 182
6.3.3 Using the jack-knife 185
6.3.4 Independent data sets 187
6.4 Conditional likelihood estimation 188
6.5 Estimation of population means 191
6.6 Estimating least-squares projections 195
Appendix A. Changing projections to equate sums of squares 197
7 Bayesian methods
7.1 Bayesian introduction 201
7.2 Spike and slab prior 203
7.3 Normal prior for regression coefficients 206
7.4 Model averaging 211
7.5 Picking the best model 215
8 Conclusions and some recommendations 217
References 223
Index 235
|
| any_adam_object | 1 |
| author | Miller, Alan |
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| dewey-full | 519.5/3621 519.5/36 |
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| dewey-search | 519.5/36 21 519.5/36 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| spelling | Miller, Alan Verfasser aut Subset selection in regression Alan Miller 2. ed. Boca Raton u.a. Chapman & Hall / CRC 2002 XVII, 238 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 95 Análise de regressão e de correlação larpcal Análise multivariada larpcal Kleinste-kwadratenmethode gtt Lineaire regressie gtt Regressieanalyse gtt Regression analysis Least squares Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Teilmenge (DE-588)4184620-5 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Methode der kleinsten Quadrate (DE-588)4038974-1 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Multiple lineare Regression (DE-588)4170718-7 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 s DE-604 Regressionsanalyse (DE-588)4129903-6 s Methode der kleinsten Quadrate (DE-588)4038974-1 s Teilmenge (DE-588)4184620-5 s 1\p DE-604 Multiple lineare Regression (DE-588)4170718-7 s 2\p DE-604 Multivariate Analyse (DE-588)4040708-1 s 3\p DE-604 Monographs on statistics and applied probability 95 (DE-604)BV002494005 95 http://www.loc.gov/catdir/toc/fy022/2002020214.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=009771631&sequence=000001&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Miller, Alan Subset selection in regression Monographs on statistics and applied probability Análise de regressão e de correlação larpcal Análise multivariada larpcal Kleinste-kwadratenmethode gtt Lineaire regressie gtt Regressieanalyse gtt Regression analysis Least squares Regressionsanalyse (DE-588)4129903-6 gnd Teilmenge (DE-588)4184620-5 gnd Multivariate Analyse (DE-588)4040708-1 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd Regressionsmodell (DE-588)4127980-3 gnd Multiple lineare Regression (DE-588)4170718-7 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4184620-5 (DE-588)4040708-1 (DE-588)4038974-1 (DE-588)4127980-3 (DE-588)4170718-7 |
| title | Subset selection in regression |
| title_auth | Subset selection in regression |
| title_exact_search | Subset selection in regression |
| title_full | Subset selection in regression Alan Miller |
| title_fullStr | Subset selection in regression Alan Miller |
| title_full_unstemmed | Subset selection in regression Alan Miller |
| title_short | Subset selection in regression |
| title_sort | subset selection in regression |
| topic | Análise de regressão e de correlação larpcal Análise multivariada larpcal Kleinste-kwadratenmethode gtt Lineaire regressie gtt Regressieanalyse gtt Regression analysis Least squares Regressionsanalyse (DE-588)4129903-6 gnd Teilmenge (DE-588)4184620-5 gnd Multivariate Analyse (DE-588)4040708-1 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd Regressionsmodell (DE-588)4127980-3 gnd Multiple lineare Regression (DE-588)4170718-7 gnd |
| topic_facet | Análise de regressão e de correlação Análise multivariada Kleinste-kwadratenmethode Lineaire regressie Regressieanalyse Regression analysis Least squares Regressionsanalyse Teilmenge Multivariate Analyse Methode der kleinsten Quadrate Regressionsmodell Multiple lineare Regression |
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