Histogram selection for possibly censored data |
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Authors: | N Akakpo C Durot |
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Institution: | 1.Laborat.Math. d’Orsay (UMR CNRS 8628),Univ. Paris Sud,Paris,France;2.Laborat.MAP5 (UMR CNRS 8145),Univ. Paris Descartes,Paris,France |
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Abstract: | We propose in this article a unified approach to functional estimation problems based on possibly censored data. The general
framework that we define allows, for instance, to handle density and hazard rate estimation based on randomly right-censored
data, or regression. Given a collection of histograms, our estimation procedure consists in selecting the best histogram among
that collection from the data, by minimizing a penalized least-squares type criterion. For a general collection of histograms,
we obtain nonasymptotic oracle-type inequalities. Then, we consider the collection of histograms built on partitions into
dyadic intervals, a choice inspired by an approximation result due to DeVore and Yu. In that case, our estimator is also adaptive
in the minimax sense over a wide range of smoothness classes that contain functions of inhomogeneous smoothness. Besides,
its computational complexity is only linear in the size of the sample. |
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Keywords: | |
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