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Stein estimation for infinitely divisible laws

Published online by Cambridge University Press:  08 September 2006

R. Averkamp  and
C. Houdré
R. Averkamp
Affiliation:
Institut für mathematische Stochastik Freiburg University Eckerstraße 1, 79104 Freiburg, Germany.
C. Houdré
Affiliation:
School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA; houdre@math.gatech.edu
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Abstract

Unbiased risk estimation, à la Stein, is studied for infinitely divisible laws with finite second moment.

Keywords

Waveletsthresholdingminimax.

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 10 , February 2006 , pp. 269 - 276
Copyright
© EDP Sciences, SMAI, 2006

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References

Averkamp, R. and Houdré, C., Wavelet Thresholding for non necessarily Gaussian Noise: Idealism. Ann. Statist. 31 (2003) 110–151.
Averkamp, R. and Houdré, C., Wavelet Thresholding for non necessarily Gaussian Noise: Functionality. Ann. Statist. 33 (2005) 2164–2193. CrossRef
Donoho, D.L and Johnstone, I.M., Adapting to Unknown Smoothness via Wavelet Shrinkage. J. Amer. Statist. Assoc. 90 (1995) 1200–1224. CrossRef
Donoho, D.L., Johnstone, I.M., Kerkyacharian, G. and Picard, D., Wavelet Shrinkage: Asymptotia? J. Roy. Statist. Soc. Ser. B 57 (1995) 301–369.
W. Feller, An Introduction to Probability Theory and its Applications, Vol. II. John Wiley & Sons (1966).
Stein, C., Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9 (1981) 1135–1151. CrossRef