Empirical Bayes Estimation With Kernel Sequence Method

In this paper, we consider the empirical Bayes estimation in the exponential family. A minimax lower bound is derived. It is shown that the best possible rate of empirical Bayes estimators is O(1/n) if Theta is bounded. Then we turn to find an empirical Bayes estimator with a rate close to this lowe...

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Bibliographic Details
Main Authors: Gupta, Shanti S, Lu, Jinjun
Format: Report
Language:English
Subjects:
BAYES THEOREM
CONVERGENCE
EMPIRICAL BAYES
EMPIRICAL BAYES INFERENCE
EXPONNENTIONAL FAMILY
INDEXES
KERNAL FUNCTIONS
KERNEL SEQUENCE METHOD
LOW RATE
MATHEMATICAL ANALYSIS
MONOTONE FUNCTIONS
RATE OF CONVERGENCE
SEQUENCES
Statistics and Probability
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Summary:In this paper, we consider the empirical Bayes estimation in the exponential family. A minimax lower bound is derived. It is shown that the best possible rate of empirical Bayes estimators is O(1/n) if Theta is bounded. Then we turn to find an empirical Bayes estimator with a rate close to this lower bound rate. Applying the kernel sequence method, we are able to construct an empirical Bayes estimator with a rate of O(1/n(1n n)7(1n 1n n)2). Under the same assumption, this rate is the fastest compared to the earlier results published in the literature.