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Wavelet based empirical Bayes estimation for the uniform distribution

โœ Scribed by Su-Yun Huang

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
268 KB
Volume
32
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

The theory of wavelets is a fast developing component in mathematics with great potential in statistical applications. In this work, we incorporate the wavelet tool into the method of empirical Bayes estimation. Asymptotic behavior of the wavelet based empirical Bayes esimator is investigated. The kernel based estimator studied by Nogami (1988) has convergence rate 0(n-1/2). We show that the wavelet based empirical Bayes estimator attains the rate 0(n-2~/(2~+ยฐ), where s ~> 1 is the regularity index of the marginal pdf ~. Derivatives considered here are distributional derivatives.

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