Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression

  title={Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression},
  author={Leonid Galtchouk and Sergey Pergamenshchikov},
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating a unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk, i.e. the asymptotic quadratic risk for this procedure coincides with the Pinsker constant which gives a sharp lower bound for the quadratic risk over all possible estimates. 1 2 1 AMS 2000 Subject Classification : primary 62G08; secondary 62G05, 62G20 2 

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
8 Extracted Citations
21 Extracted References
Similar Papers

Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 21 references

Spline smoothing in regression models and asymptotic efficiency in L2

  • Nussbaum
  • Ann. Statist
  • 1985
Highly Influential
5 Excerpts

Improved selection model method for the regression with dependent noise

  • D. Fourdrinier, Pergamenshchikov
  • Annals of the Institute of Statistical…
  • 2007

Sequential design and estimation in heteroscedastic nonparametric regression

  • S. Efromovich
  • Sequential Analysis,
  • 2007
2 Excerpts

On the asymptotic equivalence and rate of convergence of nonparametric regression and Gaussian white noise

  • Rohde
  • Statistics & Decisions
  • 2004

Risk bounds for model selection via penalization

  • A. Barron, L. Birgé, Massart
  • Probab. Theory Related Fields
  • 1999
2 Excerpts

Sharp - optimal and adaptive estimation for heteroscedastic nonparametric regression

  • S. Efromovich, Pinsker
  • Statistica Sinica,
  • 1996

Similar Papers

Loading similar papers…