Recent advances in regression methods:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York u. a.
Dekker
1981
|
| Ausgabe: | 3. print. |
| Schriftenreihe: | Statistics.
41. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003879697&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 361 S. graph. Darst. |
| ISBN: | 0824715748 |
Internformat
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| 264 | 1 | |a New York u. a. |b Dekker |c 1981 | |
| 300 | |a XII, 361 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Statistics. |v 41. | |
| 650 | 4 | |a Analyse de régression | |
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Datensatz im Suchindex
| _version_ | 1819316596588412928 |
|---|---|
| adam_text | TABLE OF CONTENTS
Preface v
1. Linear Regression Model 1
1.1 Introduction 1
1.2 Specification of the Model 2
1.3 Canonical Reduction Using Singular Value Decomposition 5
1.4 Standardization of the Model 8
1.5 A Simple Example of Two Regressors 10
Explanatory Notes 17
Exercises 25
2. Criteria for Good Regression Estimators: MSE, Consistency,
Stability, Robustness, Minimaxity and Bayesian MELO ness 29
2.1 Introduction 29
2.2 Univariate Concepts 30
2.3 Multivariate Concepts 31
2.4 Asymptotic Properties 36
2.5 Efficiency (Minimum Variance) Properties of OLS 38
2.6 Stability Properties 40
2.7 Admissibility Properties (Unbeaten Somewhere) 45
2.8 Minimax Properties 47
2.9 Acceptable Range of Shrinkage Factor for Reducing the MSE
of OLS 49
2.10 Bayes Theorem 55
Exercises 58
3. Restricted Least Squares and Bayesian Regression 61
3.1 Restricted Least Squares Estimator (RLS) 61
3.2 General Linear Hypothesis Tests 63
3.3 Properties of Restricted Estimators (RLS) 65
3.4 Mixed Regression, Stochastic Restrictions Model 70
ix
x CONTENTS
3.5 Preliminary Test Estimator (PT) 76
3.6 Bayesian Analysis of Regression 77
3.7 Inequality Restricted (IR) Least Squares Estimator 87
3.8 Need for Judgment in Empirical Research 88
Exercises 89
4. Autoregressive Moving Average (ARMA) Regression Errors
and Heteroscedasticity 90
4.1 Durbin Watson Vinod Wallis Tests 90
4.2 Tests for Regression Coefficients 93
4.3 Derivation of Bounds on F Tests Based on Eigenvalues
of a 94
4.4 Eigenvalues of Q for ARMA Processes and Tabulation of
Bounds 99
4.5 Estimation Allowing for AR(1) Errors 102
4.6 Exact DW Test Without Tables 107
4.7 Comments on MA Errors 109
4.8 Comments on General AR and/or MA processes 109
4.9 The Heteroscedasticity Problem 111
Exercises 118
5. Multicollinearity and Stability of Regression Coefficients 120
5.1 What is Multicollinearity? 120
5.2 Multicollinearity and Inestimability 123
5.3 Effects of Multicollinearity 124
5.4 An Example of the Effect of Perturbation 129
5.5 Final Remarks 129
Exercises 131
6. Stein Rule Shrinkage Estimator 134
6.1 Motivation for Shrinkage: Baseball Example 134
6.2 Stein Rule in the Regression Context 142
6.3 Properties of the Stein Rule Estimator 149
6.4 Some Extensions of the Stein Rule Estimator 153
6.5 Final Remarks 158
Explanatory Notes 159
Exercises 167
CONTENTS xi
7. Ridge Regression 169
7.1 Introduction and Historical Comments 169
7.2 Properties of the Ridge Estimator and
Choice of Biasing Parameters k 173
7.3 Bayesian and Non Bayesian Interpretation
of Ridge Methods 183
7.4 Computational Shortcuts for Ordinary Ridge 189
7.5 An Illustrative Example for Ridge Solution Selection 191
Explanatory Note 200
Exercises 203
8. Further Ridge Theory and Solutions 206
8.1 Introduction 206
8.2 Operational Values of Shrinkage Factors 208
8.3 Bias and MSE of Double f Class Generalized Ridge
Estimator 210
8.4 Bias and MSE for Operational Ordinary Ridge Estimator 213
8.5 MSE Matrix for Generalized Ridge Involving a Combination
of OLS and Restricted Least Squares Estimators 217
Explanatory Note 222
Exercises 225
9. Estimation of Polynomial Distributed Lag Models 226
9.1 Introduction 226
9.2 Estimation Under Nonstochastic Smoothness Priors 227
9.3 Estimation Under Stochastic Smoothness Priors 229
9.4 Ridge Estimation Without Smoothness Priors 237
9.5 Ridge Estimation with Nonstochastic Smoothness Priors 237
9.6 Final Remarks 238
Exercises 238
10. Multiple Sets of Regression Equations 241
10.1 Introduction 241
10.2 Seemingly Unrelated Regressions (SUR) Model 242
10.3 Temporal Cross section Model 248
10.4 Random Coefficient Regression Model 251
10.5 Lindley s Hyperparameter Model 255
Exercises 257
xii CONTENTS
11. Simultaneous Equations Model 262
11.1 Model Specification 262
11.2 Further Specifications of the System 265
11.3 Problem of Identification 267
11.4 Estimation of Structural Systems 271
11.5 Full Information Estimators 285
Exercises 289
12. Canonical Correlations, and Discriminant Analysis
with Ridge Type Modification 292
12.1 Canonical Correlations 292
12.2 Discriminant Analysis 300
Exercise 303
13. Improved Estimators Under Nonnormal Errors
and Robust Regression 305
13.1 Introduction 305
13.2 A General Class of Improved Estimators 306
13.3 Properties of 0 Under Nonnormal Disturbances 308
13.4 A Review of Minimaxity Results Under Normal
and Nonnormal Errors 313
13.5 Robust Location Estimators for Nonnormal Mean 317
13.6 Robust Regression for Nonnormal Errors 323
13.7 Iteratively Reweighted Least Squares 325
13.8 Nonnormal Errors in Multivariate Models 326
Explanatory Notes 326
Exercises 331
References 333
Index 359
|
| any_adam_object | 1 |
| author | Vinod, Hrishikesh D. 1939- Ullah, Aman 1946- |
| author_GND | (DE-588)135564700 (DE-588)112170048 |
| author_facet | Vinod, Hrishikesh D. 1939- Ullah, Aman 1946- |
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| author_sort | Vinod, Hrishikesh D. 1939- |
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| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
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| 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 |
| edition | 3. print. |
| format | Book |
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| id | DE-604.BV006138514 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T08:44:00Z |
| institution | BVB |
| isbn | 0824715748 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003879697 |
| oclc_num | 7876805 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-706 |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-706 |
| physical | XII, 361 S. graph. Darst. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Dekker |
| record_format | marc |
| series | Statistics. |
| series2 | Statistics. |
| spellingShingle | Vinod, Hrishikesh D. 1939- Ullah, Aman 1946- Recent advances in regression methods Statistics. Analyse de régression Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4129903-6 |
| title | Recent advances in regression methods |
| title_auth | Recent advances in regression methods |
| title_exact_search | Recent advances in regression methods |
| title_full | Recent advances in regression methods Hrishikesh D. Vinod ; Aman Ullah* |
| title_fullStr | Recent advances in regression methods Hrishikesh D. Vinod ; Aman Ullah* |
| title_full_unstemmed | Recent advances in regression methods Hrishikesh D. Vinod ; Aman Ullah* |
| title_short | Recent advances in regression methods |
| title_sort | recent advances in regression methods |
| topic | Analyse de régression Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Analyse de régression Regression analysis Regressionsanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003879697&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003265 |
| work_keys_str_mv | AT vinodhrishikeshd recentadvancesinregressionmethods AT ullahaman recentadvancesinregressionmethods |