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@article{561855,
author = {Řezáč, Martin},
article_location = {Bratislava},
article_number = {2},
keywords = {Kernel; density; estimate; bandwidth; maximal smoothing principle},
language = {eng},
issn = {1335-3632},
journal = {Journal of Electrical Engineering},
title = {Maximal Smoothing},
volume = {54},
year = {2003}
}
TY - JOUR
ID - 561855
AU - Řezáč, Martin
PY - 2003
TI - Maximal Smoothing
JF - Journal of Electrical Engineering
VL - 54
IS - 2
SP - 44-46
EP - 44-46
PB - Slovak University of Technology
SN - 13353632
KW - Kernel
KW - density
KW - estimate
KW - bandwidth
KW - maximal smoothing principle
N2 - Nonparametric density estimates attempt to reconstruct the probability density from which a random sample has come. A large part of the literature on density estimation is concerned with the issue of how to choose the degree of smoothness of the estimate. This paper describes the principle of maximal smoothing. The formula for asymptotically optimal bandwidth $h_f$ with respect to MISE is well-known. This formula depends on $\integral(f^{(k)}(x))^2dx$ reciprocally, where $f$ is an unknown probability density function. Our goal will be to make this integral as small as possible. Then we obtain the upper boundary for the bandwidth. The prsented paper is dealing with this procedure.
ER -
ŘEZÁČ, Martin. Maximal Smoothing. \textit{Journal of Electrical Engineering}. Bratislava: Slovak University of Technology, 2003, roč.~54, č.~2, s.~44-46. ISSN~1335-3632.
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