Related papers: Thresholding methods to estimate the copula densit…
Our article addresses the problem of flexibly estimating a multivariate density while also attempting to estimate its marginals correctly. We do so by proposing two new estimators that try to capture the best features of mixture of normals…
Density estimation is a fundamental technique employed in various fields to model and to understand the underlying distribution of data. The primary objective of density estimation is to estimate the probability density function of a random…
In this paper we study nonparametric estimators of copulas and copula densities. We first focus our study on a density copula estimator based on a polynomial orthogonal projection of the joint density. A new copula estimator is then…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…
A Copula density estimation method that is based on a finite mixture of heterogeneous parametric copula densities is proposed here. More specifically, the mixture components are Clayton, Frank, Gumbel, T, and normal copula densities, which…
This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed…
We propose a copula density estimator that can include information on bivariate marginals when the information is available. We use B-splines for copula density approximation and include information on bivariate marginals via a penalty…
One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…
In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…
We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…
Nonparametric estimation of copula density functions using kernel estimators presents significant challenges. One issue is the potential unboundedness of certain copula density functions at the corners of the unit square. Another is the…
We consider the problem of testing hypotheses on the copula density from $n$ bi-dimensional observations. We wish to test the null hypothesis characterized by a parametric class against a composite nonparametric alternative. Each density…
This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its…
Zero-inflated continuous data ubiquitously appear in many fields, in which lots of exactly zero-valued data are observed while others distribute continuously. Due to the mixed structure of discreteness and continuity in its distribution,…
This paper deals with the problem of function estimation. Using the white noise model setting, we provide a method to construct a new wavelet procedure based on thresholding rules which takes advantage of the dyadic structure of the wavelet…
We propose a new wavelet-based method for density estimation when the data are size-biased. More specifically, we consider a power of the density of interest, where this power exceeds 1/2. Warped wavelet bases are employed, where warping is…
We describe here a new method to estimate copula measure. From N observations of two variables X and Y, we draw a huge number m of subsamples (size n<N), and we compute the joint ranks in these subsamples. Then, for each bivariate rank…
This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth…
Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametrically estimating a copula density is addressed. Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable…
We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals,…