Empirical Bayes and Likelihood Inference

ISBN-13: 9780387950181 / Angielski / Miękka / 2000 / 235 str.

S. E. Ahmed; N. Reid; S. E. Ahmed

Opis

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.

Spis treści

1 Bayes/EB Ranking, Histogram and Parameter Estimation: Issues and Research Agenda.- 1 Introduction.- 2 Model and Inferential Goals.- 3 Triple-Goal Estimates.- 4 Triple Goal Evaluations.- 5 Correlated ?’s and Unequal lk.- 6 Research Agenda.- 7 References.- 2 Empirical Bayes Estimators and EM Algorithms in One-Way Analysis of Variance Situations.- 1 The Model.- 2 Some Analysis Derived From the Hierarchical Model.- 3 Large Sample Properties of the Estimates: The Collapsing Effect.- 5 The EM Algorithm in the One-Way Situation: Case ?y2 Unknown.- 6 References.- 3 EB and EBLUP in Small Area Estimation.- 1 Introduction.- 2 Type 1 Model.- 3 Type 2 Model.- 4 References.- 4 Semiparametric Empirical Bayes Estimation in Linear Models.- 1 Introduction.- 2 Preliminary Notions.- 3 Empirical Bayes Interpretations.- 4 BAN Estimators: Empirical Bayes Versions.- 5 Semiparametric Empirical Bayes Estimators.- 6 Some Concluding Remarks.- 7 References.- 5 Empirical Bayes Procedures for a Change Point Problem with Application to HIV/AIDS Data.- 1 Introduction.- 2 Gaussian Models.- 3 Estimation of Parameters.- 4 Application to the SFMHS Cohort.- 5 Discussion.- 6 References.- 6 Bayes and Empirical Bayes Estimates of Survival and Hazard Functions of a Class of Distributions.- 1 Introduction.- 2 Estimation Strategies.- 3 Numerical Results.- 4 References.- 7 Bayes and Empirical Bayes Procedures for Selecting Good Populations From a Translated Exponential Family.- 1 Introduction.- 2 Bayes and Empirical Bayes Approach.- 3 Development of Empirical Bayes Procedures.- 4 Asymptotic Optimality of the EB Procedures and Rates of Convergence.- 5 Concluding Remarks and Extension of the Results.- 6 References.- 8 Shrinkage Estimation of Regression Coefficients From Censored Data With Multiple Observations.- 1 Preliminaries and Introduction.- 2 Preliminary Test Estimation.- 3 Shrinkage Estimation.- 4 Positive-Part Shrinkage Estimation.- 5 Recommendations and Concluding Remarks.- 6 Appendix.- 7 References.- 9 Bayesian and Likelihood Inference for the Generalized Fieller-Creasy Problem.- 1 Introduction.- 2 Likelihood Based Analysis.- 3 Noninformative Priors.- 4 Propriety of Posteriors.- 5 Simulation Study and Discussion.- 6 Appendix.- 7 References.- 10 The Estimation of Ratios From Paired Data.- 1 Introduction.- 2 The Standard Analysis; Assumption (a).- 3 An Approximate Conditional Location-Scale Model; Assumption (b).- 4 A Full Location-Scale Model; Assumption (c).- 5 Examples.- 6 The Linear Functional Relationship.- 7 Discussion.- 8 References.- 11 Meta-Analysis: Conceptual Issues of Addressing Apparent Failure of Individual Study Replication or “Inexplicable” Heterogeneity.- 1 Introduction.- 2 MA and RCT Background.- 3 History Overview.- 4 Current Likelihood Based Methods for MA.- 5 Examples of EB, CL and HB Approaches.- 6 Future Directions.- 7 Initial Conclusions.- 8 A Bayesian Afterthought.- 9 Final Conclusions.- 10 Re-Analysis of Examples.- 11 What is a MA and When Should It Be Done.- 12 References.- 12 Ancillary Information for Statistical Inference.- 1 Introduction.- 2 Third Order Statistical Inference.- 3 First Derivative Ancillary.- 4 Bending and Tilting.- 5 Second Order Coordinates for a Data Component.- 6 Second Order Ancillary Directions.- 7 First Order Ancillary Directions.- 8 Examples.- 9 References.- 13 The Relevance Weighted Likelihood With Applications.- 1 Introduction.- 2 The Relevance Weighted Likelihood.- 3 Applying the NP-REWL.- 4 Applying the P-REWL.- 5 Discussion.- 6 Appendix: Proofs of the Theorems.- 7 References.