Wavelets in statistics: a review
A Antoniadis - Journal of the Italian Statistical Society, 1997 - Springer
The field of nonparametric function estimation has broadened its appeal in recent years with
an array of new tools for statistical analysis. In particular, theoretical and applied research on …
an array of new tools for statistical analysis. In particular, theoretical and applied research on …
Density estimation by wavelet thresholding
DL Donoho, IM Johnstone, G Kerkyacharian… - The Annals of …, 1996 - JSTOR
Density estimation is a commonly used test case for nonparametric estimation methods. We
explore the asymptotic properties of estimators based on thresholding of empirical wavelet …
explore the asymptotic properties of estimators based on thresholding of empirical wavelet …
[图书][B] Random fields on the sphere: representation, limit theorems and cosmological applications
D Marinucci, G Peccati - 2011 - books.google.com
Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical
random fields. The main emphasis is on tools from harmonic analysis, beginning with the …
random fields. The main emphasis is on tools from harmonic analysis, beginning with the …
[PDF][PDF] Density estimation in besov spaces zyxwvutsrqponmlkjihgfedcbazyxwvut
G Kerkyacharian, D Picard - Statistics & probability letters, 1992 - academia.edu
One can slightly modify the usual L, differentiability constraints of Sobolev types on densities
with the help of Besov norms. This has the advantage, using the wavelets characterization of …
with the help of Besov norms. This has the advantage, using the wavelets characterization of …
Estimation of smooth densities in Wasserstein distance
The Wasserstein distances are a set of metrics on probability distributions supported on
$\mathbb {R}^ d $ with applications throughout statistics and machine learning. Often, such …
$\mathbb {R}^ d $ with applications throughout statistics and machine learning. Often, such …
Wavelet-variance-based estimation for composite stochastic processes
S Guerrier, J Skaloud, Y Stebler… - Journal of the …, 2013 - Taylor & Francis
This article presents a new estimation method for the parameters of a time series model. We
consider here composite Gaussian processes that are the sum of independent Gaussian …
consider here composite Gaussian processes that are the sum of independent Gaussian …
Density estimation by kernel and wavelets methods: optimality of Besov spaces
G Kerkyacharian, D Picard - Statistics & Probability Letters, 1993 - Elsevier
This paper is showing that the saturation space of the minimax rate associated to a L p loss
and linear estimators is the Besov space B s∞ p. More precisely, it is shown that if a function …
and linear estimators is the Besov space B s∞ p. More precisely, it is shown that if a function …
Non-parametric estimation of the diffusion coefficient by wavelets methods
V Genon-Catalot, C Laredo, D Picard - Scandinavian Journal of Statistics, 1992 - JSTOR
We introduce a non-parametric estimator of the diffusion coefficient of a diffusion process
using a projection method on a wavelets orthonormal basis of L2 (R). The sample path is …
using a projection method on a wavelets orthonormal basis of L2 (R). The sample path is …
Uniform limit theorems for wavelet density estimators
Let pn (y)=∑ k α̂ k ϕ (y− k)+∑ l= 0 jn− 1∑ k β̂ lk 2 l/2 ψ (2 ly− k) be the linear wavelet
density estimator, where ϕ, ψ are a father and a mother wavelet (with compact support), α̂ …
density estimator, where ϕ, ψ are a father and a mother wavelet (with compact support), α̂ …
Minimax estimation of smooth densities in Wasserstein distance
J Niles-Weed, Q Berthet - The Annals of Statistics, 2022 - projecteuclid.org
Minimax estimation of smooth densities in Wasserstein distance Page 1 The Annals of Statistics
2022, Vol. 50, No. 3, 1519–1540 https://doi.org/10.1214/21-AOS2161 © Institute of Mathematical …
2022, Vol. 50, No. 3, 1519–1540 https://doi.org/10.1214/21-AOS2161 © Institute of Mathematical …