Abstract
This paper considers empirical Bayes (EB) squared error loss estimation (SELE) in the location family. That is, the component problem is the SELE of θ based on an observation Y having conditional (on θ) density of the form f0(y - θ) for some known density function f0. An EB estimator is constructed based on kernel type estimator of the unknown prior density using deconvolution techniques. It is shown that the proposed EB estimator is asymptotically optimal. Uniform rates of convergence of the regret are also exhibited. This paper presents a generalization to the existing results on the same problem considered for the normal (θ, 1) uniform (θ, θ + 1) and translated exponential (θ) distributions.
Original language | English (US) |
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Pages (from-to) | 435-448 |
Number of pages | 14 |
Journal | Journal of Nonparametric Statistics |
Volume | 14 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2002 |
Keywords
- Asymptotically optimal
- Bayes
- Empirical Bayes
- Kernel density estimates
- Location family
- Squared error loss estimation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty