Abstract
This part of the paper finalizes the research started in Lepski (2013b).
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References
T. Coulhon, G. Kerkyacharian, and P. Petrushev, Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2011), Manuscript.
J. Dony, U. Einmahl, and D. Mason, “Uniform in Bandwidth Consistency of Local Polynomial Regression Function Estimators”, Australian J. Statist. 35, 105–120 (2006).
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.
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).
U. Einmahl and D. M. Mason, “Uniform in Bandwidth Consistency of Kernel-Type Function Estimators”, Ann. Statist. 33(3), 1380–1403 (2005).
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).
G. Kerkyacharian, O. V. Lepski, and D. Picard, “Nonlinear Estimation in Anisotropic Multi-Index Denoising”, Probab. Theory and Relat. Fields 121, 137–170 (2001).
O. V. Lepski, “Upper Functions for Positive Random Functionals. I. General Setting and Gaussian Random Functions”, Math. Methods Statist. 22(1), 1–27 (2013a).
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).
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).
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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
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DOI: https://doi.org/10.3103/S1066530713030022