Convergence rates of empirical Bayes estimation in exponential family

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 b...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2005-04, Vol.131 (1), p.101-115
Main Authors: Li, Jianjun, Gupta, Shanti S., Liese, Friedrich
Format: Article
Language:English
Subjects:
Acceleration of convergence
Decision theory
Empirical Bayes
Exact sciences and technology
Exponential family
General topics
Kernel sequence method
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Parametric inference
Probability and statistics
Rate of convergence
Regret
Sciences and techniques of general use
Statistics
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Summary: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 O(n −1( ln n) 8) . This upper bound rate is much faster compared to the earlier results published in the literature under the same assumption.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2003.12.017