A Data-Driven Block Thresholding Approach To Wavelet Estimation
Tony Cai and Harrison Zhou
-
Abstract:
A data-driven block thresholding procedure for wavelet regression is
proposed and its theoretical and numerical properties are
investigated. The procedure empirically chooses the block size and
threshold level at each resolution level by minimizing Stein's
unbiased risk estimate. The estimator
is sharp adaptive over a class of Besov bodies and achieves
simultaneously within a small constant factor of the minimax risk over
a wide collection of Besov Bodies including both the dense and sparse
cases. The procedure is easy to implement. Numerical results show that
it has superior finite sample performance in comparison to the other
leading wavelet thresholding estimators.
- Paper:
pdf file.
- Other related papers:
Cai, T. (1999).
Adaptive wavelet estimation: a block thresholding and oracle inequality approach.
The Annals of Statistics 27, 898-924.Cai, T. & Silverman, B.W. (2001).
Incorporating information on neighboring coefficients into wavelet estimation.
Sankhya 63, 127-148.Cai, T. (2002).
On block thresholding in wavelet regression: Adaptivity, block size, and threshold level.
Statistica Sinica 12, 1241-1273.Cai, T. & Low, M. (2005).
Nonparametric function estimation over shrinking neighborhoods: Superefficiency and adaptation.
The Annals of Statistics 33, 184-213.Chicken, E. & Cai, T. (2005).
Block thresholding for density estimation: Local and global adaptivity.
J. Multivariate Analysis 95, 76-106.