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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…
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…