Block thresholding for density estimation: local and global adaptivity

Authors:
Eric Chicken;T. Tony Cai
Affiliations:
Department of Statistics, Florida State University, Tallahassee, FL 32306-4330, USA;Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104, USA
Venue:
Journal of Multivariate Analysis
Year:
2005

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Abstract

We consider wavelet block thresholding method for density estimation. A block-thresholded density estimator is proposed and is shown to achieve optimal global rate of convergence over Besov spaces and simultaneously attain the optimal adaptive pointwise convergence rate as well. These results are obtained in part through the determination of an optimal block length.