Skip to main content
Log in

Upper functions for positive random functionals. II. Application to the empirical processes theory, Part 2

  • Published:
Mathematical Methods of Statistics Aims and scope Submit manuscript

Abstract

This part of the paper finalizes the research started in Lepski (2013b).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T. Coulhon, G. Kerkyacharian, and P. Petrushev, Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2011), Manuscript.

    Google Scholar 

  2. J. Dony, U. Einmahl, and D. Mason, “Uniform in Bandwidth Consistency of Local Polynomial Regression Function Estimators”, Australian J. Statist. 35, 105–120 (2006).

    Google Scholar 

  3. J. Dony and U. Einmahl, “Uniform in Bandwidth Consistency of Kernel Regression Estimators at a Fixed Point”, in IMS Collection, Vol. 5: Highdimensional probability. The Lumini volume (2009), pp. 308–325.

    Google Scholar 

  4. U. Einmahl and D.M. Mason, “An Empirical Process Approach to the Uniform Consistency of Kernel-Type Function Estimators”, J. Theoret. Probab. 13, 1–37 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  5. U. Einmahl and D. M. Mason, “Uniform in Bandwidth Consistency of Kernel-Type Function Estimators”, Ann. Statist. 33(3), 1380–1403 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  6. E. Giné and A. Guillou, “Rate of Strong Uniform Consistency for Multivatiate Kernel Density Estimaton”, Ann. Inst. H. Poincaré, Probab. Statist. 38, 907–921 (2002).

    Article  MATH  Google Scholar 

  7. G. Kerkyacharian, O. V. Lepski, and D. Picard, “Nonlinear Estimation in Anisotropic Multi-Index Denoising”, Probab. Theory and Relat. Fields 121, 137–170 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  8. O. V. Lepski, “Upper Functions for Positive Random Functionals. I. General Setting and Gaussian Random Functions”, Math. Methods Statist. 22(1), 1–27 (2013a).

    Article  MathSciNet  MATH  Google Scholar 

  9. O. V. Lepski, “Upper Functions for Positive Random Functionals. II, Application to the Empirical Processes Theory, Part 1”, Math. Methods Statist. 22(2), 83–99 (2013b).

    Article  MathSciNet  MATH  Google Scholar 

  10. O. V. Lepski, E. Mammen, and V. G. Spokoiny, “Ideal Spatial Adaptation to Inhomogeneous Smoothness: An Approach Based on Kernel Estimates with Variable Bandwidth Selection”, Ann. Statist. 25, 929–947 (1997).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to O. Lepski.

About this article

Cite this article

Lepski, O. Upper functions for positive random functionals. II. Application to the empirical processes theory, Part 2. Math. Meth. Stat. 22, 193–212 (2013). https://doi.org/10.3103/S1066530713030022

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066530713030022

Keywords

2000 Mathematics Subject Classification

Navigation