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

  title={Adaptive density estimation of stationary β-mixing and τ-mixing processes},
  author={Matthieu Lerasle},
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.


Publications referenced by this paper.

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…