On Block Thresholding in Wavelet Regression: Adaptivity, Block Size, And Threshold Level
Tony Cai
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Abstract:
In this article we investigate the asymptotic and numerical
properties of a class of block thresholding estimators for wavelet regression.
We consider the effect of block size on global and local adaptivity
and the choice of thresholding constant. The optimal rate of convergence
for block thresholding with a given block size is derived for both the
global and local estimation. It is shown that there are conflicting requirements on the block size for achieving the global and local adaptivity.
We then consider the choice of thresholding constant for a given block size
by treating the block thresholding as a hypothesis testing problem.
The combined results lead naturally to an optimal choice
of block size and thresholding constant. We conclude with a numerical
study which compares the finite-sample performance among block thresholding
estimators as well as with other wavelet methods.
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- Other related papers:
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