Convergence rates of empirical Bayes estimation in exponential family |
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| Institution: | 1. UN A-102, 785 Jolly Road, Bldg. C Blue Bell, PA 19422, USA;2. Department of Statistics Purdue University, W. Lafayette, IN 47907, USA;3. Department of Mathematics, University of Rostock, Rostock D-18051, Germany;1. Department of Medical Physics, Hokkaido University Hospital, Sapporo, Japan;3. Department of Radiation Oncology, Hokkaido University Hospital, Sapporo, Japan;2. Department of Radiation Medicine, Hokkaido University Graduate School of Medicine, Sapporo, Japan;6. Department of Radiation Oncology, Hokkaido University Graduate School of Medicine, Sapporo, Japan;4. Global Station for Quantum Medical Science and Engineering, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Japan;1. Oregon Health & Science University, Portland, Oregon;2. NRG Oncology Statistics and Data Management Center, Philadelphia, Pennsylvania;3. Massachusetts General Hospital, Boston, Massachusetts;4. Fox Chase Cancer Center, Philadelphia, Pennsylvania;6. University of Virginia, Charlottesville, Virginia;5. University of Vermont College of Medicine, Burlington, Vermont;7. University of Alabama at Birmingham, Birmingham, Alabama;11. Cedars-Sinai Medical Center, Los Angeles, California;1. Saratov State University, 83, Astrakhanskaya str., Saratov, Russia;2. Saratov Branch of Institute of Radioengineering and Electronics of RAS, 38, Zelenaya str., Saratov, Russia;3. Yuri Gagarin State Technical University of Saratov, 77 Politechnicheskaya street, Saratov, 410054, Russia;1. Departments of Radiation Oncology, Winship Cancer Institute of Emory University, Atlanta, Georgia;2. Department of Biostatistics and Bioinformatics, Cedars-Sinai Medical Center, Los Angeles, California;3. Department of Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts;4. Department of Pediatrics, Aflac Cancer and Blood Disorders Center, Atlanta, Georgia;6. Department of Pediatrics, Massachusetts General Hospital, Boston, Massachusetts |
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| Abstract: | The convergence rates of empirical Bayes estimation in the exponential family are studied in this paper. We first develop an approach for obtaining the lower bound of empirical Bayes estimators. As an application of the approach, we demonstrate that O(n−1) is the lower bound rate for priors with bounded compact support. Second, we construct an empirical Bayes estimator using kernel sequence method and show that it has a rate of convergence of . This upper bound rate is much faster compared to the earlier results published in the literature under the same assumption. |
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