The Resource A comparison of the bayesian and frequentist approaches to estimation, Francisco J. Samaniego
A comparison of the bayesian and frequentist approaches to estimation, Francisco J. Samaniego
Resource Information
The item A comparison of the bayesian and frequentist approaches to estimation, Francisco J. Samaniego represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item A comparison of the bayesian and frequentist approaches to estimation, Francisco J. Samaniego represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 "This monograph contributes to the area of comparative statistical inference. Attention is restricted to the important subfield of statistical estimation. The book is intended for an audience having a solid grounding in probability and statistics at the level of the yearlong undergraduate course taken by statistics and mathematics majors. The necessary background on decision theory and the frequentist and Bayesian approaches to estimation is presented and carefully discussed in Chapters 13. The "threshold problem"Identifying the boundary between Bayes estimators which tend to outperform standard frequentist estimators and Bayes estimators which don'tis formulated in an analytically tractable way in Chapter 4. The formulation includes a specific (decisiontheory based) criterion for comparing estimators. The centerpiece of the monograph is Chapter 5, in which, under quite general conditions, an explicit solution to the threshold is obtained for the problem of estimating a scalar parameter under squared error loss. The six chapters that follow address a variety of other contexts in which the threshold problem can be productively treated. Included are treatments of the Bayesian consensus problem, the threshold problem for estimation problems involving of multidimensional parameters and/or asymmetric loss, the estimation of nonidentifiable parameters, empirical Bayes methods for combining data from 'similar' experiments, and linear Bayes methods for combining data from 'related' experiments. The final chapter provides an overview of the monograph's highlights and a discussion of areas and problems in need of further research."Jacket
 Language
 eng
 Extent
 1 online resource (xiii, 225 pages)
 Contents

 Cover
 A Comparison of the Bayesian and Frequentist Approaches to Estimation
 Preface
 Contents
 Chapter 1 Point Estimation from a DecisionTheoretic Viewpoint
 1.1 Tennis anyone? A glimpse at Game Theory
 1.2 Experimental data, decision rules and the risk function
 1.3 Point estimation as a decision problem; approaches to optimization
 Chapter 2 An Overview of the Frequentist Approach to Estimation
 2.1 Preliminaries
 2.2 Minimum variance unbiased estimators
 2.3 Best linear unbiased estimators
 2.4 Best invariant estimators
 2.5 Some comments on estimation within restricted classes
 2.6 Estimators motivated by their behavior in large samples
 2.7 Robust estimators of a population parameter
 Chapter 3 An Overview of the Bayesian Approach to Estimation
 3.1 Bayes8217; Theorem
 3.2 The subjectivist view of probability
 3.3 The Bayesian paradigm for data analysis
 3.4 The Bayes risk
 3.5 The class of Bayes and 8220;almost Bayes8221; rules
 3.6 The likelihood principle
 3.7 Conjugate prior distributions
 3.8 Bayesian robustness
 3.9 Bayesian asymptotics
 3.10 Bayesian computation
 3.11 Bayesian interval estimation
 Chapter 4 The Threshold Problem
 4.1 Traditional approaches to comparing Bayes and frequentist estimators
 4.1.1 Logic
 4.1.2 Objectivity
 4.1.3 Asymptotics
 4.1.4 Ease of application
 4.1.5 Admissibility
 4.1.6 The treatment of highdimensional parameters
 4.1.7 Shots across the bow
 4.2 Modeling the true state of nature
 4.3 A criterion for comparing estimators
 4.4 The threshold problem
 Chapter 5 Comparing Bayesian and Frequentist Estimators of a Scalar Parameter
 5.1 Introduction
 5.2 The wordlength experiment
 5.3 A theoretical framework
 5.4 Empirical results
 5.5 Potpourri
 5.6 Discussion
 Chapter 6 Conjugacy, SelfConsistency and Bayesian Consensus
 6.1 Another look at conjugacy
 6.2 Bayesian selfconsistency
 6.3 An approach to the consensus problem
 Chapter 7 Bayesian vs. Frequentist Shrinkage in Multivariate Normal Problems
 7.1 Preliminaries
 7.2 A solution to the threshold problem
 7.3 Discussion
 Chapter 8 Comparing Bayesian and Frequentist Estimators under Asymmetric Loss
 8.1 Introduction
 8.2 Estimating the mean of a normal distribution under Linex loss
 8.3 Estimating a linear combination of regression parameters
 8.4 Discussion
 Chapter 9 The Treatment of Nonidentifiable Models
 9.1 The classical viewpoint.
 9.2 The Bayesian treatment of nonidentifiability
 9.3 Estimation for a nonidentifiable binomial model
 9.4 On the efficacy of Bayesian updating in the binomial model
 9.5 On the efficacy of Bayesian updating in the nonparametric competing risks problem
 9.6 Bayesian estimation of a nonidentifiable parameter in a reliability context
 Chapter 10 Improving on Standard Bayesian and Frequentist Estimators
 10.1 The empirical Bayes framework
 10.2 How to be a better Bayesian
 10.3 How to be a finer frequentist
 Chapter 11 Combining Data from 8220;Related8221; Experiments
 11.1 Introduction
 11.2 A linear Bayesian approach to treating related experiments.
 11.3 Modeling and linear Bayesian inference for data fromrelated life testing experiments.
 11.4 Discussion
 Chapter 12 Fatherly Advice
 12.1 Where do I get off?
 T$29826
 Isbn
 9781441959416
 Label
 A comparison of the bayesian and frequentist approaches to estimation
 Title
 A comparison of the bayesian and frequentist approaches to estimation
 Statement of responsibility
 Francisco J. Samaniego
 Language
 eng
 Summary
 "This monograph contributes to the area of comparative statistical inference. Attention is restricted to the important subfield of statistical estimation. The book is intended for an audience having a solid grounding in probability and statistics at the level of the yearlong undergraduate course taken by statistics and mathematics majors. The necessary background on decision theory and the frequentist and Bayesian approaches to estimation is presented and carefully discussed in Chapters 13. The "threshold problem"Identifying the boundary between Bayes estimators which tend to outperform standard frequentist estimators and Bayes estimators which don'tis formulated in an analytically tractable way in Chapter 4. The formulation includes a specific (decisiontheory based) criterion for comparing estimators. The centerpiece of the monograph is Chapter 5, in which, under quite general conditions, an explicit solution to the threshold is obtained for the problem of estimating a scalar parameter under squared error loss. The six chapters that follow address a variety of other contexts in which the threshold problem can be productively treated. Included are treatments of the Bayesian consensus problem, the threshold problem for estimation problems involving of multidimensional parameters and/or asymmetric loss, the estimation of nonidentifiable parameters, empirical Bayes methods for combining data from 'similar' experiments, and linear Bayes methods for combining data from 'related' experiments. The final chapter provides an overview of the monograph's highlights and a discussion of areas and problems in need of further research."Jacket
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Samaniego, Francisco J
 Dewey number
 519.5/44
 Index
 index present
 LC call number
 QA276.8
 LC item number
 .S26 2010
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Springer Series in Statistics
 http://library.link/vocab/subjectName

 Estimation theory
 Statistical decision
 MATHEMATICS
 Statistical decision
 Mathematics
 Estimation theory
 Estimation theory
 Statistical decision
 Label
 A comparison of the bayesian and frequentist approaches to estimation, Francisco J. Samaniego
 Bibliography note
 Includes bibliographical references (pages 213219) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Cover  A Comparison of the Bayesian and Frequentist Approaches to Estimation  Preface  Contents  Chapter 1 Point Estimation from a DecisionTheoretic Viewpoint  1.1 Tennis anyone? A glimpse at Game Theory  1.2 Experimental data, decision rules and the risk function  1.3 Point estimation as a decision problem; approaches to optimization  Chapter 2 An Overview of the Frequentist Approach to Estimation  2.1 Preliminaries  2.2 Minimum variance unbiased estimators  2.3 Best linear unbiased estimators  2.4 Best invariant estimators  2.5 Some comments on estimation within restricted classes  2.6 Estimators motivated by their behavior in large samples  2.7 Robust estimators of a population parameter  Chapter 3 An Overview of the Bayesian Approach to Estimation  3.1 Bayes8217; Theorem  3.2 The subjectivist view of probability  3.3 The Bayesian paradigm for data analysis  3.4 The Bayes risk  3.5 The class of Bayes and 8220;almost Bayes8221; rules  3.6 The likelihood principle  3.7 Conjugate prior distributions  3.8 Bayesian robustness  3.9 Bayesian asymptotics  3.10 Bayesian computation  3.11 Bayesian interval estimation  Chapter 4 The Threshold Problem  4.1 Traditional approaches to comparing Bayes and frequentist estimators  4.1.1 Logic  4.1.2 Objectivity  4.1.3 Asymptotics  4.1.4 Ease of application  4.1.5 Admissibility  4.1.6 The treatment of highdimensional parameters  4.1.7 Shots across the bow  4.2 Modeling the true state of nature  4.3 A criterion for comparing estimators  4.4 The threshold problem  Chapter 5 Comparing Bayesian and Frequentist Estimators of a Scalar Parameter  5.1 Introduction  5.2 The wordlength experiment  5.3 A theoretical framework  5.4 Empirical results  5.5 Potpourri  5.6 Discussion  Chapter 6 Conjugacy, SelfConsistency and Bayesian Consensus  6.1 Another look at conjugacy  6.2 Bayesian selfconsistency  6.3 An approach to the consensus problem  Chapter 7 Bayesian vs. Frequentist Shrinkage in Multivariate Normal Problems  7.1 Preliminaries  7.2 A solution to the threshold problem  7.3 Discussion  Chapter 8 Comparing Bayesian and Frequentist Estimators under Asymmetric Loss  8.1 Introduction  8.2 Estimating the mean of a normal distribution under Linex loss  8.3 Estimating a linear combination of regression parameters  8.4 Discussion  Chapter 9 The Treatment of Nonidentifiable Models  9.1 The classical viewpoint.  9.2 The Bayesian treatment of nonidentifiability  9.3 Estimation for a nonidentifiable binomial model  9.4 On the efficacy of Bayesian updating in the binomial model  9.5 On the efficacy of Bayesian updating in the nonparametric competing risks problem  9.6 Bayesian estimation of a nonidentifiable parameter in a reliability context  Chapter 10 Improving on Standard Bayesian and Frequentist Estimators  10.1 The empirical Bayes framework  10.2 How to be a better Bayesian  10.3 How to be a finer frequentist  Chapter 11 Combining Data from 8220;Related8221; Experiments  11.1 Introduction  11.2 A linear Bayesian approach to treating related experiments.  11.3 Modeling and linear Bayesian inference for data fromrelated life testing experiments.  11.4 Discussion  Chapter 12 Fatherly Advice  12.1 Where do I get off?  T$29826
 Control code
 654397519
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 225 pages)
 Form of item
 online
 Isbn
 9781441959416
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781441959416.
 http://library.link/vocab/ext/overdrive/overdriveId
 9781441959409
 Specific material designation
 remote
 System control number
 (OCoLC)654397519
 Label
 A comparison of the bayesian and frequentist approaches to estimation, Francisco J. Samaniego
 Bibliography note
 Includes bibliographical references (pages 213219) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Cover  A Comparison of the Bayesian and Frequentist Approaches to Estimation  Preface  Contents  Chapter 1 Point Estimation from a DecisionTheoretic Viewpoint  1.1 Tennis anyone? A glimpse at Game Theory  1.2 Experimental data, decision rules and the risk function  1.3 Point estimation as a decision problem; approaches to optimization  Chapter 2 An Overview of the Frequentist Approach to Estimation  2.1 Preliminaries  2.2 Minimum variance unbiased estimators  2.3 Best linear unbiased estimators  2.4 Best invariant estimators  2.5 Some comments on estimation within restricted classes  2.6 Estimators motivated by their behavior in large samples  2.7 Robust estimators of a population parameter  Chapter 3 An Overview of the Bayesian Approach to Estimation  3.1 Bayes8217; Theorem  3.2 The subjectivist view of probability  3.3 The Bayesian paradigm for data analysis  3.4 The Bayes risk  3.5 The class of Bayes and 8220;almost Bayes8221; rules  3.6 The likelihood principle  3.7 Conjugate prior distributions  3.8 Bayesian robustness  3.9 Bayesian asymptotics  3.10 Bayesian computation  3.11 Bayesian interval estimation  Chapter 4 The Threshold Problem  4.1 Traditional approaches to comparing Bayes and frequentist estimators  4.1.1 Logic  4.1.2 Objectivity  4.1.3 Asymptotics  4.1.4 Ease of application  4.1.5 Admissibility  4.1.6 The treatment of highdimensional parameters  4.1.7 Shots across the bow  4.2 Modeling the true state of nature  4.3 A criterion for comparing estimators  4.4 The threshold problem  Chapter 5 Comparing Bayesian and Frequentist Estimators of a Scalar Parameter  5.1 Introduction  5.2 The wordlength experiment  5.3 A theoretical framework  5.4 Empirical results  5.5 Potpourri  5.6 Discussion  Chapter 6 Conjugacy, SelfConsistency and Bayesian Consensus  6.1 Another look at conjugacy  6.2 Bayesian selfconsistency  6.3 An approach to the consensus problem  Chapter 7 Bayesian vs. Frequentist Shrinkage in Multivariate Normal Problems  7.1 Preliminaries  7.2 A solution to the threshold problem  7.3 Discussion  Chapter 8 Comparing Bayesian and Frequentist Estimators under Asymmetric Loss  8.1 Introduction  8.2 Estimating the mean of a normal distribution under Linex loss  8.3 Estimating a linear combination of regression parameters  8.4 Discussion  Chapter 9 The Treatment of Nonidentifiable Models  9.1 The classical viewpoint.  9.2 The Bayesian treatment of nonidentifiability  9.3 Estimation for a nonidentifiable binomial model  9.4 On the efficacy of Bayesian updating in the binomial model  9.5 On the efficacy of Bayesian updating in the nonparametric competing risks problem  9.6 Bayesian estimation of a nonidentifiable parameter in a reliability context  Chapter 10 Improving on Standard Bayesian and Frequentist Estimators  10.1 The empirical Bayes framework  10.2 How to be a better Bayesian  10.3 How to be a finer frequentist  Chapter 11 Combining Data from 8220;Related8221; Experiments  11.1 Introduction  11.2 A linear Bayesian approach to treating related experiments.  11.3 Modeling and linear Bayesian inference for data fromrelated life testing experiments.  11.4 Discussion  Chapter 12 Fatherly Advice  12.1 Where do I get off?  T$29826
 Control code
 654397519
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 225 pages)
 Form of item
 online
 Isbn
 9781441959416
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781441959416.
 http://library.link/vocab/ext/overdrive/overdriveId
 9781441959409
 Specific material designation
 remote
 System control number
 (OCoLC)654397519
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