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Estimation of density level sets with a given probability content

Author

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  • Benoît Cadre
  • Bruno Pelletier
  • Pierre Pudlo

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.

Suggested Citation

  • Benoît Cadre & Bruno Pelletier & Pierre Pudlo, 2013. "Estimation of density level sets with a given probability content," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 261-272, March.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:261-272
    DOI: 10.1080/10485252.2012.750319
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    Cited by:

    1. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.
    2. Amaresh K Tiwari, 2021. "A Control Function Approach to Estimate Panel Data Binary Response Model," Papers 2102.12927, arXiv.org, revised Sep 2021.

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