Estimation of density level sets with a given probability content

@inproceedings{Cadrea2014EstimationOD,
  title={Estimation of density level sets with a given probability content},
  author={Beno{\^i}t Cadrea and Bruno Pelletierb and Pierre Pudloc},
  year={2014}
}
  • 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

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-4 of 4 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 16 references

Kernel estimation of density level sets

View 8 Excerpts
Highly Influenced

A Probabilistic Theory of Pattern Recognition, New-York: Springer-Verlag

L. Devroye, L. Gyorfi, G. Lugosi
Australian & New Zealand Journal of Statistics, • 1996
View 4 Excerpts
Highly Influenced

Computing and Graphing Highest Density Regions

R. Hyndman
The American Statistician, • 1996
View 3 Excerpts
Highly Influenced

Now, let J be any interval included in I . Observe that f is a locally Lipschitz function and that 1{f ∈ J} is integrable. According to Theorem 2, Chapter 3 in Evans and Gariepy

∥∇f
1992
View 5 Excerpts
Highly Influenced

Probability and Measure

P. Billingsley
Statistics and Probability Letters, • 1995
View 1 Excerpt
Highly Influenced

Total Error in a Plug-in Estimator of Level Sets

A. Baillo, A. Cuevas, A. Justel
Mathematical Society. Baillo, A • 2003

Convergence Rates in Nonparametric Estimation of Level Sets

A. Baillo, J. Cuestas-Alberto, A. Cuevas
2001
View 1 Excerpt

A Course in Differential Geometry, Providence, RI

T. Aubin
Graduate Studies in Mathematics, • 2000
View 1 Excerpt

Similar Papers

Loading similar papers…