On the L p-consistency of wavelet estimators

Authors
Liu, You Ming Xu, Jun Lian
Citation
Liu, You Ming et Xu, Jun Lian, On the L p-consistency of wavelet estimators, Acta mathematica Sinica. English series (Print) , 32(7), 2016, pp. 765-782
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
32
Issue
7
Year of publication
2016
Pages
765 - 782
Database
ACNP
SICI code
Abstract
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.