On shape-preserving wavelet estimators of cumulative distribution functions and densities
作者:
Lubomir Dechevsky,
Spiridon Penev,
期刊:
Stochastic Analysis and Applications
(Taylor Available online 1998)
卷期:
Volume 16,
issue 3
页码: 423-462
ISSN:0736-2994
年代: 1998
DOI:10.1080/07362999808809543
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
In a previous paper we introduced a general class of shapepreserving wavelet approximating operators (approximators) which transform cumulative distribution functions (cdf) and densities into functions of the same type. Empirical versions of these operators are used in this paper to introduce, in an unified way, shape- preserving wavelet estimators of cdf and densities, with a priori prescribed smoothness properties. We evaluate their risk for a variety of loss functions and analyze their asymptotic behavior. We study the convergence rates depending on minimal additional assumptions about the cdf/ density. These assumptions are in terms of the function belonging to certain homogeneous Besov or Triebel- Lizorkin spaces and others. As a main evaluation tool the integral p-modulus of smoothness is used
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