Related papers: On the estimates of the Dunkl Kernel
In this paper, we give a new approach to the theory of strictly positive kernels. Our method is based on the structure of Fock spaces. As its applications, various examples of strictly positive kernels are given. Moreover, we give a new…
We give a numerical characterization of weighted hyperplane arrangements arising from Dunkl systems.
In this note we provide a simple approximation theory motivation for the circular kernel density estimation and further explore the usefulness of the wrapped Cauchy kernel in this context. It is seen that the wrapped Cauchy kernel appears…
Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…
We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a…
The present report, has been inspired by the need of the author and its colleagues to understand the underlying theory of Wirtinger's Calculus and to further extend it to include the kernel case. The aim of the present manuscript is…
These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
The distribution of absorbed dose in radionuclide therapy with Lu$^{177}$ can be approximated by convolving an image of the time-integrated activity distribution with a dose voxel kernel representing different tissue types. This fast but…
We obtain ceratin estimates for the reproducing kernels of large weighted Bergman spaces. Applications of these estimates to boundedness of the Bergman projection on $L^p(\D,\omega ^{p/2})$, complex interpolation and duality of weighted…
We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion…
In this paper, we study the behavior of a kernel estimator of the regression function in the right censored model with $\alpha$-mixing data . The uniform strong consistency over a real compact set of the estimate is established along with a…
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…
Using the smallest eigenvalues of Hankel forms associated with a multidimensional moment problem, we establish a condition equivalent to the existence of a reproducing kernel. This result is a multivariate analogue of Berg, Chen,and…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine…
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.…
Comment on the paper of T.Bachels, H. J. G\"{u}ntherodt and R.Sch\"{a}fer : "Melting of Isolated Tin Nanoparticles".