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Ideal Spatial Adaptation by Wavelet Shrinkage
Minimax estimation sub ject to doing well at a point Orthogonal Wavelet Bases of Compact Support
2015/8/20
With ideal spatial adaptation, an oracle furnishes information about how best to
adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial,
variable knot spline, or vari...
WAVELET SHRINKAGE FOR CORRELATED DATA AND INVERSE PROBLEMS: ADAPTIVITY RESULTS
Adaptation correlated data fractional brownian motion
2015/8/20
Johnstone and Silverman (1997) described a level-dependent thresholding
method for extracting signals from correlated noise. The thresholds were chosen
to minimize a data based unbiased risk criteri...
We attempt to recover an unknown function from noisy, sampled data. Using
orthonormal bases of compactly supported wavelets we develop a nonlinear method
which works in the wavelet domain by simple ...
We discuss a method for curve estimation based on n noisy
data; one translates the empirical wavelet coecients towards the origin by
an amount p
2 log(n) =p
n. The method is nearly minimax for...
Adapting to Unknown Smoothness via Wavelet Shrinkage
Minimax Decision theory Stein's Unbiased Estimate of Risk
2015/8/20
We attempt to recover a function of unknown smoothness from noisy, sampled
data. We introduce a procedure, SureShrink, which suppresses noise by thresholding
the empirical wavelet coecients. The th...
Considerable e ort has been directed recently to develop asymptotically minimax methods in problems of recovering in nite-dimensional ob jects (curves, densities, spectral densities, images) from nois...