scholarly journals A sharp oracle inequality for Graph-Slope

2017 ◽  
Vol 11 (2) ◽  
pp. 4851-4870 ◽  
Author(s):  
Pierre C. Bellec ◽  
Joseph Salmon ◽  
Samuel Vaiter
Keyword(s):  
Oracle Inequality

scholarly journals Oracle Inequality for a Statistical Raus--Gfrerer-Type Rule

2013 ◽  
Vol 1 (1) ◽  
pp. 386-407 ◽  
Author(s):  
Qinian Jin ◽  
Peter Mathé
Keyword(s):  
Oracle Inequality

scholarly journals Estimating the conditional density by histogram type estimators and model selection

2017 ◽  
Vol 21 ◽  
pp. 34-55
Author(s):  
Mathieu Sart
Keyword(s):  
Model Selection ◽  
Type Inequality ◽  
Estimation Procedure ◽  
Conditional Density ◽  
Distributed Data ◽  
Oracle Inequality ◽  
Random Partition ◽  
Selection Theorem ◽  
Piecewise Constant ◽  
Anisotropic Besov Spaces

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).

scholarly journals Stable Recovery of Sparse Signals and an Oracle Inequality

2010 ◽  
Vol 56 (7) ◽  
pp. 3516-3522 ◽  
Author(s):  
Tony Tony Cai ◽  
Lie Wang ◽  
Guangwu Xu
Keyword(s):  
Sparse Signals ◽  
Oracle Inequality
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