Estimation of density level sets with a given probability content

Benoît Cadre, Bruno Pelletier and Pierre Pudlo

Journal of Nonparametric Statistics, 2013, vol. 25, issue 1, 261-272

Abstract: Given a random vector X valued in ℝ-super- d with density f and an arbitrary probability number p ∈(0; 1), we consider the estimation of the upper level set> texlscub > f ≥ t -super-( p )>/ texlscub >of f corresponding to probability content p , that is, such that the probability that X belongs to> texlscub > f ≥ t -super-( p )>/ texlscub >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 is a random threshold depending on the sample and [fcirc] 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.

Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1080/10485252.2012.750319

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