Improving efficiency by shrinkage: the James-Stein and ridge regression estimators
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1998
|
| Series: | Statistics
156 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Teilw. zugl.: Rochester, NY, Univ. of Rochester, Diss. |
| Physical Description: | XII, 632 S. graph. Darst. |
| ISBN: | 0824701569 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface
v
Part I Introduction to Shrinkage Estimators
Chapter I. Introduction
1
1.0
Motivation for Writing This Book
1
1.1
Purpose of This Book
4
1.2
Introduction to the James-Stein Estimator (JS)
5
1.3
Introduction to the Ridge Regression Estimator
7
1.4
Historical Survey
15
1.5
Empirical
Bayes
Methodology
61
1.6
A Minimum Mean Square Error Estimator,
Its Approximation as an Empirical
Bayes
Estimator
66
1.7
The Structure of This Book
68
Chapter II. The Stein Paradox
71
2.0
Estimation of the Mean
71
2.1
The Multivariate Normal Distribution
73
2.2
Maximum Likelihood Estimation
76
2.3
The Decision Theory Framework
81
2.4
Why the MLE May Not Be the Best
84
2.5
Another Case Against the MLE
91
ix
Contents
2.6 ThelnadmissibilityoftheMLE 93
2.7 The JS
as an Empirical
Bayes
Estimator
(EBE)
99
2.8.
How the JS is a Special Case of the Operational Ridge
Regression Estimator
104
2.9
Introduction to the Positive Part of the JS
107
2.10
Summary
110
Chapter III. The Ridge Estimators of Hoerl and Kennard 111
3.0
The Need for Alternatives to the
Least Square Estimators
111
3.1
Derivation of the Ridge Estimator
112
3.2
The Efficiency of the Ridge Regression Estimator
117
3.3
Estimating the Ridge Perturbation Factor k-
The Ridge Trace
133
3.4
Estimating the Ridge Perturbation Factor k-
Objective Methods
141
3.5
Evaluation of the Efficiency of Ridge Estimators
by Computer Simulation
158
3.6
Summary
166
Part II Estimation for a Single Linear Model
Chapter IV. James-Stein Estimators for a Single Linear Model
167
4.0
Introduction
167
4.1
Review of Basic Linear Model Concepts
169
4.2
The James-Stein Estimator from a
Bayesian Point of View
173
4.3
The Non-Bayesian Formulation of the JS and the JSL
186
4.4
The Average Mean Square Error
(MSE)
190
4.5
The Conditional
MSE
195
4.6
The
MSE
of the JS for Different Quadratic
Loss Functions
202
4.7
The Efficiency of the JS as Compared with
Optimum Estimators
206
4.8
Summary
223
4.9
Appendix
223
Contents xi
Chapter V. Ridge Estimators from Different Points of View
227
5.0
Introduction
227
5.1
Some More Review of Linear Models
229
5.2
The Generalized Ridge Regression Estimator
240
5.3
The Mixed Estimators
242
5.4
The Linear Minimax Estimator
248
5.5
The Linear
Bayes
Estimator
250
5.6
Comparing the Efficiency of the Ridge and
the Least Square Estimator from the
Frequentist Point of View
266
5.7
Comparing the
MSE
of Ridge-Type
Estimators from the Bayesian Point of View
284
5.8
The Jack-knifed Ridge Estimator
298
5.9
Summary
305
Chapter VI. Improving the James-Stein Estimator: The Positive Parts
307
307
309
312
337
364
370
371
371
373
387
403
413
418
432
439
Chapter
VIII.
The Precision of Individual Estimators
441
8.0
Introduction
441
8.1
The Mean of a Multivariate Normal Distribution
442
8.2
The Single Linear Model
448
6.0
Introduction
6.1
The Positive Parts of the James-Stein
Estimator (PP0
-
PP4)
6.2
The Average Mean Square Error
6.3
The Conditional Mean Square Error
6.4
The Estimators of Shao and Strawderman
6.5
Summary
Part III Other Linear Model Setups
Chapter
VII
.
The Simultaneous Estimation Problem
7.0
Introduction
7.1
The
EBE
of
С
R.Rao
7.2
The
EBE
of Wind
7.3
The Estimator of Dempster
7.4
A Generalization of the
EBE
7.5
Comparing the Efficiency of the Estimators
7.6
The Positive Parts
7.7
Summary
xn
Contents
8.3
The Case of
r
Linear Models
458
8.4
The Limited Translation Estimators
480
8.5
Summary
490
Chapter IX. The
Multi
variate
Linear Model
491
9.0
Introduction
491
9.1
The Multivariate Linear Model
493
9.2
The BE
496
9.3
The
EBE
of Wind for One Linear Model
500
9.4
The
EBE
for
r
Linear Models
512
9.5
The Estimator of Dempster
(An Example of an Approximate
MSE)
525
9.6
Summary
529
Chapter X. Other Linear Model Setups
531
10.0
Introduction
531
10.1
The Seemingly Unrelated Regression Model (SURE)
533
10.2
Some Aspects of the Simultaneous Estimation Problem
542
10.3
The
Kalman
Filter
556
10.4
Summary
578
Chapter XI. Summary and Conclusion
579
11.0
Introduction
579
11.1
Overview of the Chapters
580
11.2
Conclusion
590
References
591
Author Index
619
Subject Index
625
about the book
. ..
This well-targeted reference/text offers a unified treatment of different kinds of
James-Stein and ridge regression estimators from a frequentist and Bayesian point of
view.
Self-contained for practitioners and students with a background in linear models,
Improving Efficiency by Shrinkage explains and compares estimators both analyti¬
cally and numerically and includes
Mathematica
and Maple programs used in nu¬
merical comparison.
.
.provides a historical survey of a vast amount of literature on the
subject...demonstrates why, when, and where ridge regression estimators are ad¬
vantageous.
.
.furnishes a proof of the inadmissibility of the James-Stein estimator.
..
illustrates how shrinkage estimators solve applied problems...addresses practical
issues in the study of ridge estimators...contrasts efficiencies with the least square
estimator...shows how to improve the efficiency of James-Stein estimators by using
positive parts.
.
.and more.
With nearly
1300
equations, bibliographic citations, and figures, Improving Effi¬
ciency by Shrinkage is an outstanding reference for applied statisticians, engineers,
econometricians, sociologists, psychologists, data analysts, biometricians, and medi¬
cal researchers and an excellent text for graduate-level courses in regression, linear
models, and econometrics as well as seminars in statistics.
|
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| spelling | Gruber, Marvin H. Verfasser aut Improving efficiency by shrinkage the James-Stein and ridge regression estimators Marvin H. J. Gruber New York [u.a.] Dekker 1998 XII, 632 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics 156 Teilw. zugl.: Rochester, NY, Univ. of Rochester, Diss. Schätztheorie (DE-588)4121608-8 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Regressionsmodell (DE-588)4127980-3 s Schätztheorie (DE-588)4121608-8 s DE-604 Statistics 156 (DE-604)BV000003265 156 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008081750&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008081750&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Gruber, Marvin H. Improving efficiency by shrinkage the James-Stein and ridge regression estimators Statistics Schätztheorie (DE-588)4121608-8 gnd Regressionsmodell (DE-588)4127980-3 gnd |
| subject_GND | (DE-588)4121608-8 (DE-588)4127980-3 (DE-588)4113937-9 |
| title | Improving efficiency by shrinkage the James-Stein and ridge regression estimators |
| title_auth | Improving efficiency by shrinkage the James-Stein and ridge regression estimators |
| title_exact_search | Improving efficiency by shrinkage the James-Stein and ridge regression estimators |
| title_full | Improving efficiency by shrinkage the James-Stein and ridge regression estimators Marvin H. J. Gruber |
| title_fullStr | Improving efficiency by shrinkage the James-Stein and ridge regression estimators Marvin H. J. Gruber |
| title_full_unstemmed | Improving efficiency by shrinkage the James-Stein and ridge regression estimators Marvin H. J. Gruber |
| title_short | Improving efficiency by shrinkage |
| title_sort | improving efficiency by shrinkage the james stein and ridge regression estimators |
| title_sub | the James-Stein and ridge regression estimators |
| topic | Schätztheorie (DE-588)4121608-8 gnd Regressionsmodell (DE-588)4127980-3 gnd |
| topic_facet | Schätztheorie Regressionsmodell Hochschulschrift |
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