Related papers: Multiwavelet density estimation
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
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…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
The aim of this paper is to show the usefulness of Meyer wavelets for the classical problem of density estimation and for density deconvolution from noisy observations. By using such wavelets, the computation of the empirical wavelet…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient…
We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a…
Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…
Multivariate kernel density estimations have received much spate of interest. In addition to conventional methods of (non-)classical associated-kernels for (un)bounded densities and bandwidth selections, the multiple extended-beta kernel…
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…
This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel.…
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 review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
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…
We propose a new statistical procedure able in some way to overcome the curse of dimensionality without structural assumptions on the function to estimate. It relies on a least-squares type penalized criterion and a new collection of models…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation…
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…
We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…