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> Volume 4, Issue 4
Preprint: Preprints from the IRISA ftp host (A. Juditsky)

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Anatoli Iouditski Guest

Posted: Mon Dec 02, 2002 6:07 pm Subject: Preprint: Preprints from the IRISA ftp host (A. Juditsky)




Preprint: Preprints from the IRISA ftp host (A. Juditsky)
title: Wavelet Estimators, Global Error Measures Revisited
author: Bernard Delyon, Anatoli Juditsky
Abstract: In the paper minimax rates of convergence for
wavelet estimators are studied. For the problems of density estimation and
nonparametric regression we establish upper bounds over a large range of
functional classes and global error measures.
The constructed estimate is simultaneously minimax (up to constant) for
all L_pi error
measures, 0
ftp: irisa.irisa.fr: /techreports/1993/PI782.ps.Z
title: Wavelet Estimators: Adapting to Unknown Smoothness
author: Anatoli Juditsky
Abstract: A wavelet thresholding algorithm is used to recover
a function of unknown smoothness from noisy data. It is known that
it can be
tuned to be minimax in order over a wide range of Besovtype
smoothness constraints and L_plosses. We provide a method
to estimate an adaptive threshold parameter for each resolution level.
It is shown that the proposed algorithm is {em adaptive in order}, i.e.
it attains the rate of convergence which is minimax up to a constant over
Besov regularity classes and L_perror measures, 1<=p<= infinity.
The algorithm is computationally straightforward: the whole effort to compute
the threshold is order N log(N) for the sample size N.
ftp: irisa.irisa.fr: /techreports/1994/PI815.ps.Z
title: On the Computation of Wavelet Coefficients
author: Bernard Delyon, Anatoli Juditsky
Abstract: We consider fast algorithms of wavelet decomposition
of function f when
discrete observations of f (supp(f) belongs to [0,1]) are available.
The properties of the algorithms are studied
for three types of observation design: the regular design,
when the observations f(x_i) are
taken on the regular grid x_i=i/N, i=1, ..., N; the case of gittered regular
grid, when
it is only known that for all 0< i< N+1, i/N<= x_i<(i+1)/N;
the random design case: x_i, i=1, ..., N are
independent and identically distributed random variables on [0,1].
We show that these algorithms are in certain sense efficient when the accuracy
of approximation is concerned.
The proposed algorithms are computationally straightforward: the whole
effort to compute
the decomposition is order N for the sample size N.
ftp: irisa.irisa.fr: /techreports/1994/PI856.ps.Z
title: Computing wavelet density estimator for stochastic processes
author: Anatoli Juditsky, Frederique Leblanc
Abstract: Let (X_t) be a stictly stationary stochastic process (in continuous or discrete time). We are to estimate the density f of X_t on the basis
of discrete observations (X_i), i=1,..., N using a "linear" wavelet
estimator.
For the continuous time process (X_t), 0<= t<= T those observations
are the result of a regular discretization of
the continuous time trajectory.
We provide an adaptive version of the algorithm, which adapts automatically to
the regularity parameters of the density f. To compute the estimator we implement a fast algorithm (the whole effort to compute the estimate is order N log(N)
for the sample size N). 





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