Sign based methods in linear statistical models:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
1997
|
| Schriftenreihe: | Translations of mathematical monographs
162 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 234 S. graph. Darst. |
| ISBN: | 0821803719 |
Internformat
MARC
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| 100 | 1 | |a Boldin, Michail V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Sign based methods in linear statistical models |c M. V. Boldin ; G. I. Simonova ; Yu. N. Tyurin |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1997 | |
| 300 | |a XII, 234 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 162 | |
| 650 | 4 | |a Linear models (Statistics) | |
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| 700 | 1 | |a Tjurin, Jurij N. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804138211311616000 |
|---|---|
| adam_text | Contents
Preface xi
Introduction 1
Part 1. Linear Models of Independent Observations
Chapter 1. Sign-based analysis of one-parameter linear regression 13
1.1. Hubble s Law: A historical overview 13
1.2. Determination of the Hubble constant by the sign-based method 16
1.3. Asymptotic results 26
1.4. The influence function 33
Chapter 2. Sign tests 35
2.1. General linear model 35
2.2. Locally optimal sign tests in the regression problem 38
2.3. Evaluation of critical values: Asymptotic theory 44
2.4. Example: Two-way layout 46
2.5. Computation of critical values: Finite samples 48
Chapter 3. Sign estimators 51
3.1. Sign estimators and their computation 51
3.2. Sign estimation: Asymptotic theory 60
3.2.1. The role of asymptotic theory 60
3.2.2. Consistency of sign estimators 61
3.2.3. Asymptotic normality of sign estimators 64
3.2.4. Asymptotic covariance of sign estimators 68
3.2.5. Uniform law of large numbers 68
3.2.6. Theorem on uniform linearity 71
3.2.7. Asymptotic power of sign tests 76
3.2.8. Sensitivity curve 76
3.3. Comparison of estimators 77
3.3.1. How estimators are compared 77
3.3.2. Rank estimation 79
3.3.3. Least squares and least absolute deviations estimators 81
3.3.4. Asymptotic efficiency of sign estimators 82
Chapter 4. Testing linear hypotheses 85
4.1. Sign procedures for testing linear hypotheses 85
4.2. Asymptotic properties of sign tests for linear hypotheses 87
4.3. Examples 90
vii
viii CONTENTS
4.4. Testing linear hypotheses in one- and two-way layout problems 93
4.5. Computation of critical values in testing linear hypotheses 97
Part 2. Linear Models of Time Series
Introduction to Part 2 107
Chapter 5. Least squares and least absolute deviations procedures in
the simplest autoregressive model 109
5.1. Introduction 109
5.2. The simplest stationary autoregressive equation and its solutions 110
5.3. Least squares procedures 112
5.3.1. Least squares estimator 113
5.3.2. Tests based on the LSE 115
5.4. Least squares estimator in nonstationary autoregression 119
5.5. Least absolute deviations procedures 121
5.5.1. Least absolute deviations estimator 121
5.5.2. Tests based on the LAD estimator 124
5.5.3. Weighted least absolute deviations estimators 127
5.6. Influence functionals of least squares and least absolute deviations
estimators 129
5.6.1. Influence functional of the least squares estimator 131
5.6.2. Influence functional of the LAD estimator 132
5.6.3. Influence functional of weighted LAD estimators 133
5.7. Testing for stationarity of the autoregression process 134
5.8. Proofs 138
Chapter 6. Sign-based analysis of one-parameter autoregression 143
6.1. Introduction to sign-based autoregression analysis 143
6.2. Sign tests 147
6.3. Sign tests in a nonstationary autoregression 151
6.4. Uniform stochastic expansion: The power of sign tests under local
alternatives 154
6.5. Sign tests: Comparison with other nonparametric tests 157
6.6. Sign estimators 161
6.6.1. Sign estimator /3Uis 161
6.6.2. Sign estimator /?* s 164
6.6.3. Sign estimator /?„}$ 165
6.7. Influence functionals of sign estimators 166
6.7.1. Influence functional of the sign estimator /?„,£ 166
6.7.2. Influence functional of the sign estimator /?„,# 170
6.7.3. Influence functional of the sign estimator /?* s 170
6.8. Simulation results: Evaluation of quantiles, confidence sets, and
contaminated samples 171
6.8.1. Evaluation of quantiles 171
6.8.2. Confidence estimation of (3 175
6.8.3. Sign estimation from contaminated samples 179
6.9. Proof of Theorem 6.4.1 181
CONTENTS ix
Chapter 7. Sign-based analysis of the multiparameter autoregression 193
7.1. Introduction 193
7.2. Test statistics and their null distributions 196
7.3. Uniform stochastic expansion: The power of sign tests under local
alternatives 202
7.4. Testing linear hypotheses 206
7.5. Sign-based estimators 208
7.5.1. Sign estimator J3n s 209
7.5.2. Sign estimator J3n s 210
7.5.3. Sign estimator/3*5 211
7.6. Influence functionals of estimators in the multiparameter autore¬
gression 213
7.6.1. Influence functional of the least squares estimator 214
7.6.2. Influence functional of the least absolute deviations estimator 215
7.6.3. Influence functionals of weighted LAD estimators 217
7.6.4. Influence functional of the sign estimator /3n s 217
7.6.5. Influence functional of the sign estimator f3*s 218
7.7. Empirical distribution function of residuals and related empirical
processes 219
7.8. Proof of Theorem 7.7.1 225
Bibliography 231
|
| adam_txt |
Contents
Preface xi
Introduction 1
Part 1. Linear Models of Independent Observations
Chapter 1. Sign-based analysis of one-parameter linear regression 13
1.1. Hubble's Law: A historical overview 13
1.2. Determination of the Hubble constant by the sign-based method 16
1.3. Asymptotic results 26
1.4. The influence function 33
Chapter 2. Sign tests 35
2.1. General linear model 35
2.2. Locally optimal sign tests in the regression problem 38
2.3. Evaluation of critical values: Asymptotic theory 44
2.4. Example: Two-way layout 46
2.5. Computation of critical values: Finite samples 48
Chapter 3. Sign estimators 51
3.1. Sign estimators and their computation 51
3.2. Sign estimation: Asymptotic theory 60
3.2.1. The role of asymptotic theory 60
3.2.2. Consistency of sign estimators 61
3.2.3. Asymptotic normality of sign estimators 64
3.2.4. Asymptotic covariance of sign estimators 68
3.2.5. Uniform law of large numbers 68
3.2.6. Theorem on uniform linearity 71
3.2.7. Asymptotic power of sign tests 76
3.2.8. Sensitivity curve 76
3.3. Comparison of estimators 77
3.3.1. How estimators are compared 77
3.3.2. Rank estimation 79
3.3.3. Least squares and least absolute deviations estimators 81
3.3.4. Asymptotic efficiency of sign estimators 82
Chapter 4. Testing linear hypotheses 85
4.1. Sign procedures for testing linear hypotheses 85
4.2. Asymptotic properties of sign tests for linear hypotheses 87
4.3. Examples 90
vii
viii CONTENTS
4.4. Testing linear hypotheses in one- and two-way layout problems 93
4.5. Computation of critical values in testing linear hypotheses 97
Part 2. Linear Models of Time Series
Introduction to Part 2 107
Chapter 5. Least squares and least absolute deviations procedures in
the simplest autoregressive model 109
5.1. Introduction 109
5.2. The simplest stationary autoregressive equation and its solutions 110
5.3. Least squares procedures 112
5.3.1. Least squares estimator 113
5.3.2. Tests based on the LSE 115
5.4. Least squares estimator in nonstationary autoregression 119
5.5. Least absolute deviations procedures 121
5.5.1. Least absolute deviations estimator 121
5.5.2. Tests based on the LAD estimator 124
5.5.3. Weighted least absolute deviations estimators 127
5.6. Influence functionals of least squares and least absolute deviations
estimators 129
5.6.1. Influence functional of the least squares estimator 131
5.6.2. Influence functional of the LAD estimator 132
5.6.3. Influence functional of weighted LAD estimators 133
5.7. Testing for stationarity of the autoregression process 134
5.8. Proofs 138
Chapter 6. Sign-based analysis of one-parameter autoregression 143
6.1. Introduction to sign-based autoregression analysis 143
6.2. Sign tests 147
6.3. Sign tests in a nonstationary autoregression 151
6.4. Uniform stochastic expansion: The power of sign tests under local
alternatives 154
6.5. Sign tests: Comparison with other nonparametric tests 157
6.6. Sign estimators 161
6.6.1. Sign estimator /3Uis 161
6.6.2. Sign estimator /?* s 164
6.6.3. Sign estimator /?„}$ 165
6.7. Influence functionals of sign estimators 166
6.7.1. Influence functional of the sign estimator /?„,£ 166
6.7.2. Influence functional of the sign estimator /?„,# 170
6.7.3. Influence functional of the sign estimator /?* s 170
6.8. Simulation results: Evaluation of quantiles, confidence sets, and
contaminated samples 171
6.8.1. Evaluation of quantiles 171
6.8.2. Confidence estimation of (3 175
6.8.3. Sign estimation from contaminated samples 179
6.9. Proof of Theorem 6.4.1 181
CONTENTS ix
Chapter 7. Sign-based analysis of the multiparameter autoregression 193
7.1. Introduction 193
7.2. Test statistics and their null distributions 196
7.3. Uniform stochastic expansion: The power of sign tests under local
alternatives 202
7.4. Testing linear hypotheses 206
7.5. Sign-based estimators 208
7.5.1. Sign estimator J3n s 209
7.5.2. Sign estimator J3n s 210
7.5.3. Sign estimator/3*5 211
7.6. Influence functionals of estimators in the multiparameter autore¬
gression 213
7.6.1. Influence functional of the least squares estimator 214
7.6.2. Influence functional of the least absolute deviations estimator 215
7.6.3. Influence functionals of weighted LAD estimators 217
7.6.4. Influence functional of the sign estimator /3n s 217
7.6.5. Influence functional of the sign estimator f3*s 218
7.7. Empirical distribution function of residuals and related empirical
processes 219
7.8. Proof of Theorem 7.7.1 225
Bibliography 231 |
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| author | Boldin, Michail V. Simonova, Galina I. Tjurin, Jurij N. |
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| dewey-search | 519.5/35 21 |
| dewey-sort | 3519.5 235 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:38:11Z |
| indexdate | 2024-07-09T21:24:35Z |
| institution | BVB |
| isbn | 0821803719 |
| language | English |
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| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Boldin, Michail V. Verfasser aut Sign based methods in linear statistical models M. V. Boldin ; G. I. Simonova ; Yu. N. Tyurin Providence, RI American Mathematical Society 1997 XII, 234 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 162 Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd rswk-swf Nichtparametrisches Verfahren (DE-588)4339273-8 gnd rswk-swf Lineares Modell (DE-588)4134827-8 s Nichtparametrisches Verfahren (DE-588)4339273-8 s DE-604 Simonova, Galina I. Verfasser aut Tjurin, Jurij N. Verfasser aut Translations of mathematical monographs 162 (DE-604)BV000002394 162 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016879307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boldin, Michail V. Simonova, Galina I. Tjurin, Jurij N. Sign based methods in linear statistical models Translations of mathematical monographs Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd |
| subject_GND | (DE-588)4134827-8 (DE-588)4339273-8 |
| title | Sign based methods in linear statistical models |
| title_auth | Sign based methods in linear statistical models |
| title_exact_search | Sign based methods in linear statistical models |
| title_exact_search_txtP | Sign based methods in linear statistical models |
| title_full | Sign based methods in linear statistical models M. V. Boldin ; G. I. Simonova ; Yu. N. Tyurin |
| title_fullStr | Sign based methods in linear statistical models M. V. Boldin ; G. I. Simonova ; Yu. N. Tyurin |
| title_full_unstemmed | Sign based methods in linear statistical models M. V. Boldin ; G. I. Simonova ; Yu. N. Tyurin |
| title_short | Sign based methods in linear statistical models |
| title_sort | sign based methods in linear statistical models |
| topic | Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd |
| topic_facet | Linear models (Statistics) Lineares Modell Nichtparametrisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016879307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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