On the L ^sup p^-consistency of wavelet estimators

This paper deals with the L p-consistency of wavelet estimators for a density function based on size-biased random samples. More precisely, we firstly show the L p-consistency of wavelet estimators for independent and identically distributed random vectors in Rd. Then a similar result is obtained fo...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2016-07, Vol.32 (7), p.765
Main Authors: Liu, You Ming, Xu, Jun Lian
Format: Article
Language:English
Subjects:
Applied mathematics
Mathematical functions
Mathematical models
Mathematics
Random variables
Studies
Theorems
Online Access:Get full text
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Summary:This paper deals with the L p-consistency of wavelet estimators for a density function based on size-biased random samples. More precisely, we firstly show the L p-consistency of wavelet estimators for independent and identically distributed random vectors in Rd. Then a similar result is obtained for negatively associated samples under the additional assumptions d = 1 and the monotonicity of the weight function.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-5392-8