Kernel and wavelet density estimators on manifolds and more general metric spaces
| Autor: | Pencho Petrushev, Athanasios G. Georgiadis, Dominique Picard, Gerard Kerkyacharian, Galatia Cleanthous |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Pure mathematics Mathematics - Statistics Theory Statistics Theory (math.ST) 01 natural sciences Ahlfors regularity sample kernel density estimators Functional calculus 010104 statistics & probability Wavelet FOS: Mathematics 0101 mathematics Besov space Heat kernel Mathematics non-parametric estimators Probability (math.PR) 010102 general mathematics Estimator Primary 62G07 58J35 Secondary 43A85 42B35 wavelet density estimators Nonlinear system Metric space heat kernel Kernel (statistics) adaptive density estimators Mathematics - Probability |
| Zdroj: | 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 |
| Popis: | 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 of smooth functional calculus with well localized spectral kernels, Besov regularity spaces, and wavelet type systems. Kernel and both linear and nonlinear wavelet density estimators are introduced and studied. Convergence rates for these estimators are established, which are analogous to the existing results in the classical setting of real-valued variables. |
| Databáze: | OpenAIRE |
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