Rates of Convergence in Empirical Bayes Estimation Problems: Continuous Case
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In this article, a sequence of empirical Bayes estimators for a density function and its derivatives, which are not assumed to be uniformly bounded, using classes of kernel functions is proposed.Abstract:
In this paper we construct sequences of estimators for a density function and its derivatives, which are not assumed to be uniformly bounded, using classes of kernel functions. Utilizing these estimators, a sequence of empirical Bayes estimators is proposed. It is found that this sequence is asymptotically optimal in the sense of Robbins (Ann. Math. Statist. 35 (1964) 1-20). The rates of convergence of the Bayes risks associated with the proposed empirical Bayes estimators are obtained. It is noted that the exact rate is $n^{-q}$ with $q \leqq \frac{1}{3}$. An example is given and an explicit kernel function is indicated.read more
Citations
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Empirical Bayes Estimation in Lebesgue-Exponential Families with Rates Near the best Possible Rate
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Empirical Bayes with rates and best rates of convergence in u(x)C(θ) exp(-x/θ)-family: Estimation case
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References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications.
Book ChapterDOI
An Empirical Bayes Approach to Statistics
TL;DR: In this paper, a random variable with a priori distribution function is considered, and a probability distribution depending in a known way on an unknown real parameter A, where A is assumed to have discrete values.
Journal ArticleDOI
The Empirical Bayes Approach to Statistical Decision Problems
TL;DR: The empirical Bayes approach is applicable when the same decision problem presents itself repeatedly and independently with a fixed but unknown a priori distribution of the parameter as mentioned in this paper, which is the case of statistical decision problems in practice.
Book
Empirical Bayes methods
TL;DR: In this article, empirical Bayes rules for a variety of special models are described and the problem of assessing the goodness of an empirical estimator for a given set of prior data is addressed.