Related papers: Thresholding methods to estimate the copula densit…
In this paper, we investigate the almost sure convergence, in supremum norm, of the rank-based linear wavelet estimator for a multivariate copula density. Based on empirical process tools, we prove a uniform limit law for the deviation,…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
A new nonparametric model of maximum-entropy (MaxEnt) copula density function is proposed, which offers the following advantages: (i) it is valid for mixed random vector. By `mixed' we mean the method works for any combination of discrete…
Assume that $(X_t)_{t\in\Z}$ is a real valued time series admitting a common marginal density $f$ with respect to Lebesgue's measure. Donoho {\it et al.} (1996) propose a near-minimax method based on thresholding wavelets to estimate $f$ on…
A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by…
In this work, we study wavelet projection estimators for density estimation, focusing on their construction from $\mathcal{S}$-regular, compactly supported wavelet bases. A key aspect of such estimators is the choice of the resolution…
For signals belonging to balls in smoothness classes and noise with enough moments, the asymptotic behavior of the minimax quadratic risk among soft-threshold estimates is investigated. In turn, these results, combined with a median…
Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging…
Parametric factor copula models typically work well in modeling multivariate dependencies due to their flexibility and ability to capture complex dependency structures. However, accurately estimating the linking copulas within these models…
This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding…
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…
This paper deals with the classical problem of density estimation on the real line. Most of the existing papers devoted to minimax properties assume that the support of the underlying density is bounded and known. But this assumption may be…
We propose a new approach towards approximating the density-to-pair-density map based on copula theory from statistics. We extend the copula theory to multi-dimensional marginals, and deduce that one can describe any (exact or approximate)…
Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…
This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the…
We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric…
In this paper, we study the problem of pointwise estimation of a multivariate density. We provide a data-driven selection rule from the family of kernel estimators and derive for it a pointwise oracle inequality. Using the latter bound, we…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and…
The purpose of this paper is to introduce two semiparametric methods for the estimation of copula parameter. These methods are based on minimum Alpha-Divergence between a non-parametric estimation of copula density using local likelihood…