Estimation of density level sets with a given probability content

  title={Estimation of density level sets with a given probability content},
  author={Beno{\^i}t Cadrea and Bruno Pelletierb and Pierre Pudloc},
  • Benoît Cadrea, Bruno Pelletierb, Pierre Pudloc
  • Published 2014
Given a random vector X valued in Rd with density f and an arbitrary probability number p ∈ (0; 1), we consider the estimation of the upper level set {f ≥ t(p)} of f corresponding to probability content p, that is, such that the probability that X belongs to {f ≥ t(p)} is equal to p. Based on an i.i.d. random sample X1, . . . , Xn drawn from f , we define the plug-in level set estimate {f̂n ≥ t n }, where t n is a random threshold depending on the sample and f̂n is a nonparametric kernel… CONTINUE READING

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