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Ideal Denoising in an orthonormal basis chosen from a library of bases
Wavelet Packets Cosine Packets weak-` p spaces
2015/8/20
Suppose we have observations yi = si +zi, i = 1; :::; n, where (si) is signal and (zi)
is i.i.d. Gaussian white noise. Suppose we have available a library L of orthogonal
bases, such as the Wavelet ...
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...
Consider estimating the mean vector from data Nn(; 2I ) with lq norm loss,
q 1, when is known to lie in an n-dimensional lp ball, p 2 (0; 1). For large
n, the ratio of minimax linear risk to...
On minimax estimation of a sparse normal mean vector
nearly black object robustness white noise model
2015/8/20
Mallows has conjectured that among distributions which are Gaussian but
for occasional contamination by additive noise, the one having least Fisher
information has (two-sided) geometric contaminatio...
Minimax Bayes, asymptotic minimax and sparse wavelet priors
Minimax Decision theory Minimax Bayes estimation
2015/8/20
Pinsker(1980) gave a precise asymptotic evaluation of the minimax mean squared
error of estimation of a signal in Gaussian noise when the signal is known a priori
to lie in a compact ellipsoid in Hi...
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of
data in the form of n observations (or cases) of a vector with p variables. Contemporary data sets
of...
This paper explores a class of empirical Bayes methods for levedependent threshold selection in wavelet shrinkage. The prior considered
for each wavelet coefficient is a mixture of an atom of p...
Wavelet deconvolution in a periodic setting
Adaptive estimation Deconvolution Meyer wavelet
2015/8/20
Deconvolution problems are naturally represented in the Fourier domain, whereas
thresholding in wavelet bases is known to have broad adaptivity properties. We study a method
which combines both fast...
NEEDLES AND STRAW IN HAYSTACKS: EMPIRICAL BAYES ESTIMATES OF POSSIBLY SPARSE SEQUENCES
HAYSTACKS NEEDLES AND STRAW
2015/8/20
An empirical Bayes approach to the estimation of possibly sparse
sequences observed in Gaussian white noise is set out and investigated. The
prior considered is a mixture of an atom of probability a...
The purpose of model selection algorithms such as All Subsets, Forward Selection,
and Backward Elimination is to choose a linear model on the basis of the same set of
data to which the model will be...
We study soft threshold estimates of the non-centrality parameter ξ of a non-central χ2
d(ξ)
distribution, of interest, for example, in estimation of the squared length of the mean of a
Gaussian ve...
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...
ASYMPTOTIC MINIMAXITY OF WAVELET ESTIMATORS WITH SAMPLED DATA
Besov spaces bounded operators between Besov spaces
2015/8/20
Donoho and Johnstone (1998) studied a setting where data were obtained
in the continuum white noise model and showed that scalar nonlinearities applied
to wavelet coefficients gave estimators w...
Wavelets have motivated development of a host of new ideas in nonparametric
regression smoothing. Here we apply the tool of exact risk analysis, to understand the
small sample behavior of wavelet es...
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 ...