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Abstract:
By developing the classical kernel method, Delaigle and Meister provide a nice estimation for a density function with some Fourier-oscillating noises over a Sobolev ball W-2(s)(L) and over L-2 risk (Delaigle and Meister in Stat. Sin. 21: 1065-1092, 2011). The current paper extends their theorem to Besov ball B-r,q(s)(L) and L-p risk with p, q, r is an element of [1,infinity] by using wavelet methods. We firstly show a linear wavelet estimation for densities in B-r,q(s)(L) over L-p risk, motivated by the work of Delaigle and Meister. Our result reduces to their theorem, when p = q = r = 2. Because the linear wavelet estimator is not adaptive, a nonlinear wavelet estimator is then provided. It turns out that the convergence rate is better than the linear one for r <= p. In addition, our conclusions contain estimations for density derivatives as well.
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JOURNAL OF INEQUALITIES AND APPLICATIONS
ISSN: 1029-242X
Year: 2014
1 . 6 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
ESI HC Threshold:81
JCR Journal Grade:2
CAS Journal Grade:3
Cited Count:
WoS CC Cited Count: 4
SCOPUS Cited Count: 7
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 7
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