On Adaptive Wavelet Estimation of a Derivative And Other Related Linear Inverse Problems
Tony Cai
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Abstract:
We consider a block thresholding and vaguelet-wavelet approach to certain
statistical linear inverse problems. Based on an oracle inequality, an
adaptive block thresholding estimator for linear inverse problems
is proposed and the asymptotic properties of the estimator are
investigated. It is shown that the estimator enjoys a higher degree of
adaptivity than the standard term-by-term thresholding methods;
it attains the exact optimal rates of convergence over a range of
Besov classes. The problem of estimating a derivative is considered in
more detail as a test for the general estimation procedure. We show
that the derivative estimator is spatially adaptive; it automatically
adapts to the local smoothness of the function and attains the local
adaptive minimax rate for estimating a derivative at a point.
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- Other related papers:
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