anisotropic besov spaces
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2020 ◽  
Vol 49 (3) ◽  
pp. 863-896 ◽  
Author(s):  
Jahangir Cheshmavar ◽  
Hartmut Führ


2020 ◽  
Vol 106 (2) ◽  
pp. 18-30
Author(s):  
N.T. Tleukhanova ◽  
K.K. Sadykov




2017 ◽  
Vol 21 ◽  
pp. 34-55
Author(s):  
Mathieu Sart

We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By using a deterministic Hellinger distance as loss, we prove that the selected function satisfies a non-asymptotic oracle type inequality under minimal assumptions on the statistical setting. We derive an adaptive piecewise constant estimator on a random partition that achieves the expected rate of convergence over (possibly inhomogeneous and anisotropic) Besov spaces of small regularity. Moreover, we show that this oracle inequality may lead to a general model selection theorem under very mild assumptions on the statistical setting. This theorem guarantees the existence of estimators possessing nice statistical properties under various assumptions on the conditional density (such as smoothness or structural ones).







2012 ◽  
Vol 396 (1) ◽  
pp. 21-48 ◽  
Author(s):  
Mourad Ben Slimane ◽  
Hnia Ben Braiek


2012 ◽  
Vol 80 (1-2) ◽  
pp. 179-198
Author(s):  
B. Barrios ◽  
Jorge J. Betancor


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