Empirical Bayes and Likelihood Inference

by Ahmed, S. E.; Reid, N.

• ISBN13: 9780387950181
• ISBN10: 0387950184
• Format: Paperback
• Copyright: 2000-10-01
• Publisher: Springer Nature

Summary

Bayesian and likelihood approaches to inference have a number of points of close contact, especially from an asymptotic point of view. Both approaches emphasize the construction of interval estimates of unknown parameters. Empirical Bayes methods have historically emphasized instead the construction of point estimates. In this volume researchers present recent work on several aspects of Bayesian, likelihood and empirical Bayes methods, presented at a workshop held in Montreal, Canada. The goal of the workshop was to explore the linkages among the methods, and to suggest new directions for research in the theory of inference.

Table of Contents

List of Contributors	xiii
Bayes/EB Ranking, Histogram and Parameter Estimation: Issues and Research Agenda	1	(16)
T. A. Louis
Introduction	1	(1)
Model and Inferential Goals	2	(2)
Triple-Goal Estimates	4	(1)
Triple Goal Evaluations	5	(4)
Correlated &thetas;'s and Unequal lk	9	(3)
Research Agenda	12	(3)
References	15	(2)
Empirical Bayes Estimators and EM Algorithms in One-Way Analysis of Variance Situations	17	(16)
I Guttman
The Model	17	(1)
Some Analysis Derived From the Hierarchical Model	18	(3)
Large Sample Properties of the Estimates: The Collapsing Effect	21	(2)
Mean Square Considerations	23	(4)
The EM Algorithm in the One-Way Situation: Case σ2y Unknown	27	(5)
References	32	(1)
EB and EBLUP in Small Area Estimation	33	(12)
J. N. K. Rao
Introduction	33	(2)
Type 1 Model	35	(4)
Type 2 Model	39	(2)
References	41	(4)
Semiparametric Empirical Bayes Estimation in Linear Models	45	(22)
P. K. Sen
Introduction	45	(1)
Preliminary Notions	46	(2)
Empirical Bayes Interpretations	48	(4)
BAN Estimators: Empirical Bayes Versions	52	(3)
Semiparametric Empirical Bayes Estimators	55	(6)
Some Concluding Remarks	61	(2)
References	63	(4)
Empirical Bayes Procedures for a Change Point Problem with Application to HIV/AIDS Data	67	(14)
S.-L. T. Normand
K. Doksum
Introduction	67	(1)
Gaussian Models	68	(3)
Estimation of Parameters	71	(2)
Application to the SFMHS Cohort	73	(4)
Discussion	77	(1)
References	78	(3)
Bayes and Empirical Bayes Estimates of Survival and Hazard Functions of a Class of Distributions	81	(8)
M. Ahsanullah
S. E. Ahmed
Introduction	81	(1)
Estimation Strategies	82	(3)
Numerical Results	85	(2)
References	87	(2)
Bayes and Empirical Bayes Procedures for Selecting Good Populations From a Translated Exponential Family	89	(14)
R. S. Singh
Introduction	89	(2)
Bayes and Empirical Bayes Approach	91	(2)
Development of Empirical Bayes Procedures	93	(3)
Asymptotic Optimality of the EB Procedures and Rates of Convergence	96	(3)
Concluding Remarks and Extension of the Results	99	(1)
References	99	(4)
Shrinkage Estimation of Regression Coefficients From Censored Data With Multiple Observations	103	(18)
S. E. Ahmed
Preliminaries and Introduction	103	(7)
Preliminary Test Estimation	110	(4)
Shrinkage Estimation	114	(2)
Positive-Part Shrinkage Estimation	116	(2)
Recommendations and Concluding Remarks	118	(1)
Appendix	119	(1)
References	119	(2)
Bayesian and Likelihood Inference for the Generalized Fieller---Creasy Problem	121	(20)
M. Yin
M. Ghosh
Introduction	121	(2)
Likelihood Based Analysis	123	(2)
Noninformative Priors	125	(3)
Propriety of Posteriors	128	(2)
Simulation Study and Discussion	130	(5)
Appendix	135	(2)
References	137	(4)
The Estimation of Ratios From Paired Data	141	(20)
D. A. Sprott
Introduction	141	(2)
The Standard Analysis; Assumption (a)	143	(2)
An Approximate Conditional Location-Scale Model; Assumption (b)	145	(2)
A Full Location-Scale Model; Assumption (c)	147	(3)
Examples	150	(4)
The Linear Functional Relationship	154	(2)
Discussion	156	(2)
References	158	(3)
Meta-Analysis: Conceptual Issues of Addressing Apparent Failure of Individual Study Replication or ``Inexplicable'' Heterogeneity	161	(24)
K. O'Rourke
Introduction	161	(2)
MA and RCT Background	163	(1)
History Overview	164	(2)
Current Likelihood Based Methods for MA	166	(1)
Examples of EB, CL and HB Approaches	167	(3)
Future Directions	170	(2)
Initial Conclusions	172	(1)
A Bayesian Afterthought	173	(1)
Final Conclusions	174	(1)
Re-Analysis of Examples	175	(4)
What is a MA and When Should It Be Done	179	(1)
References	180	(5)
Ancillary Information for Statistical Inference	185	(26)
D. A. S. Fraser
N. Reid
Introduction	185	(2)
Third Order Statistical Inference	187	(2)
First Derivative Ancillary	189	(3)
Bending and Tilting	192	(3)
Second Order Coordinates for a Data Component	195	(2)
Second Order Ancillary Directions	197	(3)
First Order Ancillary Directions	200	(4)
Examples	204	(3)
References	207	(4)
The Relevance Weighted Likelihood With Applications	211	(23)
F. Hu
J. V. Zidek
Introduction	211	(1)
The Relevance Weighted Likelihood	212	(4)
Applying the NP-REWL	216	(5)
Applying the P-REWL	221	(4)
Discussion	225	(1)
Appendix: Proofs of the Theorems	226	(8)
References	234