Monotone Empirical Bayes Estimators Based on More Informative Samples

References

• Clayton , D. and Kaldor , J. 1987 . “Empirical Bayes Estimates of Age-Standardized Relative Risks for Use in Disease Mapping,” . Biometrics , 43 : 671 – 681 .
   PubMed Web of Science ®Google Scholar
• Cressie , N. 1982 . “A Useful Empirical Bayes Identity,” . The Annals of Statistics , 10 : 625 – 629 .
   Web of Science ®Google Scholar
• Collins , R. and Langman , M. 1985 . “Treatment With Histamine H2 Antagonist in Acute Gastrointestinal Hemorrhage,” . New England Journal of Medicine , 313 : 660 – 666 .
   PubMed Web of Science ®Google Scholar
• Dempster , A. P. , Laird , N. M. and Rubin , D. B. 1977 . “Maximum Likelihood From Incomplete Data Via the EM Algorithm” . Journal of the Royal Statistical Society , 39 : 1 – 38 . (with discussion), Ser. B
   Google Scholar
• DerSimonian , R. and Laird , N. M. 1986 . “Meta-Analysis in Clinical Trials,” . Controlled Clinical Trials , 7 : 177 – 188 .
   PubMedGoogle Scholar
• Laird , N. M. 1978 . “Nonparametric Maximum Likelihood Estimation of a Mixing Distribution,” . Journal of the American Statistical Association , 73 : 805 – 811 .
   Web of Science ®Google Scholar
• Manton , K. G. , Woodbury , M. A. , Stallard , E. , Riggan , W. B. , Creason , J. P. and Pellom , A. C. 1989 . “Empirical Bayes Procedures for Stabilizing Maps of U.S.A. Cancer Mortality Rates,” . Journal of the American Statistical Association , 84 : 637 – 650 .
   PubMed Web of Science ®Google Scholar
• Mollie , A. and Richardson , S. 1991 . “Empirical Bayes Estimates of Cancer Mortality Rates Using Spatial Models,” . Statistics in Medicine , 10 : 95 – 112 .
   PubMed Web of Science ®Google Scholar
• Morris , C. N. 1983a . “Parametric Empirical Bayes Inference: Theory and Applications,” . Journal of the American Statistical Association , 78 : 47 – 55 .
   Web of Science ®Google Scholar
• Morris , C. N. 1983b . “Natural Exponential Families With Quadratic Variance Functions: Statistical Theory,” . The Annals of Statistics , 11 : 515 – 529 .
   Web of Science ®Google Scholar
• O'Bryan , T. 1979 . “Rates of Convergence in a Modified Empirical Bayes Problem Involving Poisson Distributions,” . Communications in Statistics, Part A—Theory and Methods , 8 : 167 – 174 .
   Web of Science ®Google Scholar
• Robbins , H. “An Empirical Bayes Approach to Statistics,” . Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability . pp. 157 – 164 .
   Google Scholar
• Robbins , H. 1963 . “The Empirical Bayes Approach to Testing Statistical Hypotheses,” . Review of the International Statistical Institute , 31 : 195
   Google Scholar
• Robbins , H. 1964 . “The Empirical Bayes Approach to Statistical Problems,” . The Annals of Mathematical Statistics , 35 : 1 – 20 .
   Google Scholar
• Singh , R. S. 1979 . “Empirical Bayes Estimation in Lebesgue-Exponential Families With Rates Near the Best Possible Rate,” . The Annals of Statistics , 7 : 890 – 902 .
   Web of Science ®Google Scholar
• Stijnen , T. and van Houwelingen , J. C. 1990 . “Empirical Bayes Methods in Clinical Trials Meta-Analysis,” . Biometrical Journal , 32 : 335 – 346 .
   Web of Science ®Google Scholar
• Thomas , D. C. , Siemictycki , J. , Dewar , R. , Robins , J. , Goldberg , M. and Armstrong , B. G. 1985 . “The Problem of Multiple Inference in Studies Designed to Generate Hypotheses,” . American Journal of Epidemiology , 122 : 1080 – 1095 .
   PubMed Web of Science ®Google Scholar
• van Houwelingen , J. C. 1973 . “On Empirical Bayes Rules for the Continuous Exponential Family,” , doctoral dissertation Dept. of Mathematics, Utrecht University .
   Google Scholar
• van Houwelingen , J. C. 1977 . “Monotonizing Empirical Bayes Estimators for a Class of Discrete Distributions With Monotone Likelihood Ratio,” . Statistica Neerlandica , 31 : 95 – 104 .
   Google Scholar