Kernel and wavelet density estimators on manifolds and more general metric spaces

Autor: Pencho Petrushev, Athanasios G. Georgiadis, Dominique Picard, Gerard Kerkyacharian, Galatia Cleanthous

Publikováno v: Cleanthous, G, Georgiadis, A, Kerkyacharian, G, Petrushev, P & Picard, D 2018 ' Kernel and wavelet density estimators on manifolds and more general metric spaces ' arXiv . < https://arxiv.org/abs/1805.04682 >
Bernoulli 26, no. 3 (2020), 1832-1862

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 development

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https://vbn.aau.dk/da/publications/68c2ac95-a895-4946-a76e-68a2cf5dcd36

Capturing Ridge Functions in High Dimensions from Point Queries

Autor: Albert Cohen, Dominique Picard, Gerard Kerkyacharian, Ingrid Daubechies, Ronald A. DeVore

Publikováno v: Constructive Approximation. 35:225-243

Constructing a good approximation to a function of many variables suffers from the “curse of dimensionality”. Namely, functions on ℝN with smoothness of order s can in general be captured with accuracy at most O(n−s/N) using linear spaces or

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https://doi.org/10.1007/s00365-011-9147-6

Regularity of Gaussian Processes on Dirichlet spaces

Autor: Shigeyoshi Ogawa, Dominique Picard, Gerard Kerkyacharian, Pencho Petrushev

Publikováno v: Constructive Approximation
Constructive Approximation, 2018, Constructive Approximation, 47 (2), pp.277-320. ⟨10.1007/s00365-018-9416-8⟩

We study the regularity of centered Gaussian processes $$(Z_x( \omega ))_{x\in M}$$ , indexed by compact metric spaces $$(M, \rho )$$ . It is shown that the almost everywhere Besov regularity of such a process is (almost) equivalent to the Besov regu

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Dicussion on the Meeting on ‘Statistical Approaches to Inverse Problems’

Autor: Eero Saksman, Dominique Picard, S Meng, F Ruymgaart, David J. Evans, Manfred Opper, G Wahba, Robert G. Aykroyd, L Cavalier, Manuel Davy, Heikki Haario, Ad Stoffelen, Sofia C. Olhede, Daniela De Canditiis, Simon J. Godsill, Felix Abramovich, Christophe Andrieu, Guy P. Nason, Patrick J. Wolfe, Markku Lehtinen, Lehel Csató, Dan Cornford, C Butucea, Eric Moulines, D Paul, Gerard Kerkyacharian, E Khabie-Zeitoune, Marko Laine, Marianna Pensky, Alexandre B. Tsybakov, Johanna Tamminen, Marc Raimondo, Robert West, Ross N. Hoffman, W Ng, U Golubev, Noel A Cressie, Iain M. Johnstone, Christian P. Robert, Axel Munk

Publikováno v: Journal of the Royal Statistical Society Series B: Statistical Methodology. 66:627-652

Johnstone, Kerkyacharian, Picard and Raimondo Johnstone, Kerkyacharian, Picard and Raimondo are interested in the inverse problem of estimating f where f has been convolved with g and then contaminated with white noise. This popular problem has been

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https://doi.org/10.1111/j.1467-9868.2004.2060d.x

Thomas Bayes' walk on manifolds

Autor: Ismaël Castillo, Dominique Picard, Gerard Kerkyacharian

Publikováno v: Probability Theory and Related Fields
Probability Theory and Related Fields, Springer Verlag, 2014, 158 (3-4), pp.665-710
Probability Theory and Related Fields, 2014, 158 (3-4), pp.665-710. ⟨10.1007/s00440-013-0493-0⟩

International audience; Convergence of the Bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold, or more generally on a compact metric space verifying some c

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a9f43441bf16399a3faff316e6631e7
https://hal.archives-ouvertes.fr/hal-00976006