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Statements

Subject Item
n2:RIV%2F00216224%3A14310%2F07%3A00022321%21RIV10-MSM-14310___
rdf:type
n7:Vysledek skos:Concept
dcterms:description
The most commonly used nonparametric estimate of a cumulative distribution function F is an empirical distribution function F_n. But F_n is a step function even in case that F is continuous. The present paper aims to provide a smooth estimate of F. Kernel methods seem to be adequate for this purpose. There exist several methods how to choose a bandwidth. We propose a method of bandwidth selection based on a suitable estimate of Mean Integrated Square Error. We also focus on an estimate of a cumulative distribution function in case that random variables X_1,...,X_n are nonnegative. The aforementioned methods are not reliable near the point x=0. In order to avoid this problem we propose a~reflection method. A simulation study is conducted to compare the performance of the different methods of bandwidth choice. Theoretical results are applied to the data concerning the content of toxic material in the fish population in Lake Ontario. The most commonly used nonparametric estimate of a cumulative distribution function F is an empirical distribution function F_n. But F_n is a step function even in case that F is continuous. The present paper aims to provide a smooth estimate of F. Kernel methods seem to be adequate for this purpose. There exist several methods how to choose a bandwidth. We propose a method of bandwidth selection based on a suitable estimate of Mean Integrated Square Error. We also focus on an estimate of a cumulative distribution function in case that random variables X_1,...,X_n are nonnegative. The aforementioned methods are not reliable near the point x=0. In order to avoid this problem we propose a~reflection method. A simulation study is conducted to compare the performance of the different methods of bandwidth choice. Theoretical results are applied to the data concerning the content of toxic material in the fish population in Lake Ontario.
dcterms:title
Smooth Estimates of Distribution Functions with Application in Environmental Studies Smooth Estimates of Distribution Functions with Application in Environmental Studies
skos:prefLabel
Smooth Estimates of Distribution Functions with Application in Environmental Studies Smooth Estimates of Distribution Functions with Application in Environmental Studies
skos:notation
RIV/00216224:14310/07:00022321!RIV10-MSM-14310___
n3:aktivita
n17:P
n3:aktivity
P(LC06024)
n3:dodaniDat
n11:2010
n3:domaciTvurceVysledku
n16:3062023 n16:5407656 n16:2811294
n3:druhVysledku
n15:O
n3:duvernostUdaju
n9:S
n3:entitaPredkladatele
n14:predkladatel
n3:idSjednocenehoVysledku
450547
n3:idVysledku
RIV/00216224:14310/07:00022321
n3:jazykVysledku
n10:eng
n3:klicovaSlova
cumulative distribution function; kernel smoothing; reflection method
n3:klicoveSlovo
n4:cumulative%20distribution%20function n4:reflection%20method n4:kernel%20smoothing
n3:kontrolniKodProRIV
[65DB00B6CD79]
n3:obor
n13:BA
n3:pocetDomacichTvurcuVysledku
3
n3:pocetTvurcuVysledku
4
n3:projekt
n6:LC06024
n3:rokUplatneniVysledku
n11:2007
n3:tvurceVysledku
El-Shaarawi, Abdel H. Koláček, Jan Horová, Ivanka Zelinka, Jiří
n5:organizacniJednotka
14310