Wavelet optimal estimations for a two-dimensional continuous-discrete density function over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L^{p}$\end{document}Lp risk
The mixed continuous-discrete density model plays an important role in reliability, finance, biostatistics, and economics. Using wavelets methods, Chesneau, Dewan, and Doosti provide upper bounds of wavelet estimations on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepa...
Saved in:
Published in | Journal of inequalities and applications Vol. 2018; no. 1 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.01.2018
|
Online Access | Get full text |
Cover
Loading…
Summary: | The mixed continuous-discrete density model plays an important role in reliability, finance, biostatistics, and economics. Using wavelets methods, Chesneau, Dewan, and Doosti provide upper bounds of wavelet estimations on
\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$L^{2}$\end{document}
L
2
risk for a two-dimensional continuous-discrete density function over Besov spaces
\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$B^{s}_{r,q}$\end{document}
B
r
,
q
s
. This paper deals with
\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$L^{p}$\end{document}
L
p
(
\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$1\leq p < \infty$\end{document}
1
≤
p
<
∞
) risk estimations over Besov space, which generalizes Chesneau–Dewan–Doosti’s theorems. In addition, we firstly provide a lower bound of
\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$L^{p}$\end{document}
L
p
risk. It turns out that the linear wavelet estimator attains the optimal convergence rate for
\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$r \geq p$\end{document}
r
≥
p
, and the nonlinear one offers optimal estimation up to a logarithmic factor. |
---|---|
ISSN: | 1025-5834 1029-242X |
DOI: | 10.1186/s13660-018-1868-7 |