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Estimation of density level sets with a given probability content

Abstract : Given a random vector X valued in R^d with density f and an arbitrary probability number p in (0; 1), we consider the estimation of the upper level set of f corresponding to probability content p, that is, such that the probability that X belongs to it is equal to p. Based on an i.i.d. random sample X_1, ..., X_n drawn from f, we define the plug-in level set estimate, where t_n^(p) is a random threshold depending on the sample and f_n is a nonparametric kernel density estimate based on the same sample. We establish the exact convergence rate of the Lebesgue measure of the symmetric difference between the estimated and actual level sets.
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https://hal.archives-ouvertes.fr/hal-00796621
Contributor : Pierre Pudlo <>
Submitted on : Monday, March 4, 2013 - 3:53:07 PM
Last modification on : Saturday, July 11, 2020 - 3:18:02 AM

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Benoît Cadre, Bruno Pelletier, Pierre Pudlo. Estimation of density level sets with a given probability content. Journal of Nonparametric Statistics, American Statistical Association, 2013, 25 (1), pp.261-272. ⟨10.1080/10485252.2012.750319⟩. ⟨hal-00796621⟩

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