54 citations · 57 across the 8 of their papers we have counts for
10 papers
Rate-optimal and computationally efficient nonparametric estimation on the circle and the sphere
Athanasios G. Georgiadis, Andrew P. Percival
We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that…
Adaptive estimation of the -norm of a probability density and related topics II. Upper bounds via the oracle approach
Galatia Cleanthous, Athanasios G. Georgiadis, Oleg V. Lepski
This is the second part of the research project initiated in Cleanthous et al (2024). We deal with the problem of the adaptive estimation of the -norm of a probabilit…
Adaptive estimation of -norm of a probability density and related topics I. Lower bounds
Galatia Cleanthous, Athanasios G. Georgiadis, Oleg V. Lepski
We deal with the problem of the adaptive estimation of the -norm of a probability density on , , from independent observations. The unknown den…
Spaces of distributions on product metric spaces associated with operators
Athanasios G. Georgiadis, George Kyriazis, Pencho Petrushev
We lay down the foundation of the theory of spaces of distributions on the product of doubling metric measure spaces , in the presence of non-negative se…
Pointwise density estimation on metric spaces and applications in seismology
Galatia Cleanthous, Athanasios G. Georgiadis, Philip A. White
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 frame…
Minimax Density Estimation on Sobolev Spaces With Dominating Mixed Smoothness
Galatia Cleanthous, Athanasios G. Georgiadis, Emilio Porcu
We study minimax density estimation on the product space . We consider -risk for probability density functions defined over regularity…
Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators
Athanasios G. Georgiadis, Gerard Kerkyacharian, George Kyriazis +1
We deal with homogeneous Besov and Triebel-Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kern…
Kernel and wavelet density estimators on manifolds and more general metric spaces
G. Cleanthous, A. Georgiadis, G. Kerkyacharian +2
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…
Fourier Multipliers on Anisotropic Mixed-Norm Spaces of Distributions
Galatia Cleanthous, Athanasios G. Georgiadis, Morten Nielsen
A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizo…
Wavelet transforms for homogeneous mixed-norm Triebel--Lizorkin spaces
A. G. Georgiadis, J. Johnsen, M. Nielsen
Homogeneous mixed-norm Triebel--Lizorkin spaces are introduced and studied with the use of a discrete wavelet transformation, the so-called -transform. This extends the classica…