Adaptive density estimation of stationary β-mixing and τ-mixing processes

@inproceedings{Lerasle2009AdaptiveDE,
  title={Adaptive density estimation of stationary β-mixing and τ-mixing processes},
  author={Matthieu Lerasle},
  year={2009}
}
We propose an algorithm to estimate the common density s of a stationary process X1, ..., Xn. We suppose that the process is either β or τ -mixing. We provide a model selection procedure based on a generalization of Mallows’ Cp and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
SHOWING 1-10 OF 26 REFERENCES

Inequalities for absolutely regular sequences: application to density estimation

  • Gabrielle Viennet
  • Probab. Theory Related Fields,
  • 1997
Highly Influential
6 Excerpts

Random walks with stationary increments and renewal theory, volume 112 of Mathematical Centre Tracts

  • Henry C.P. Berbee
  • Mathematisch Centrum,
  • 1979
Highly Influential
4 Excerpts

New dependence coefficients. Examples and applications to statistics

  • Jérôme Dedecker, Clémentine Prieur
  • Probab. Theory Related Fields,
  • 2005
Highly Influential
9 Excerpts

Similar Papers

Loading similar papers…