Related papers: Nonparametric needlet estimation for partial deriv…
This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of…
Nonparametric density estimators are studied for $d$-dimensional, strongly spatial mixing data which is defined on a general $N$-dimensional lattice structure. We consider linear and nonlinear hard thresholded wavelet estimators which are…
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…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
The problem of estimating a probability density function f on the (d-1)-dimensional unit sphere S^{d-1} from directional data using the needlet frame is considered. It is shown that the decay of needlet coefficients supported near a point…
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…
In the random coefficients binary choice model, a binary variable equals 1 iff an index $X^\top\beta$ is positive.The vectors $X$ and $\beta$ are independent and belong to the sphere $\mathbb{S}^{d-1}$ in $\mathbb{R}^{d}$.We prove lower…
This paper investigates the nonparametric estimation of a heteroskedastic variance function on the sphere in a regression framework, assuming the variance belongs to a Besov regularity class. A needlet-based estimator is proposed, combining…
The paper deals with the problem of nonparametric estimating the $L_p$--norm, $p\in (1,\infty)$, of a probability density on $R^d$, $d\geq 1$ from independent observations. The unknown density %to be estimated is assumed to belong to a ball…
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…
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…
Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They…
We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…
Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…
We study the problem of nonparametric estimation under $\bL_p$-loss, $p\in [1,\infty)$, in the framework of the convolution structure density model on $\bR^d$. This observation scheme is a generalization of two classical statistical models,…
We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport. These estimators represent the measure of interest as the pushforward of a chosen reference…
Reconstruction of sets from a random sample of points intimately related to them is the goal of set estimation theory. Within this context, a particular problem is the one related with the reconstruction of density level sets and…
Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…
We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…
This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We…