About: Smooth Estimates of Distribution Functions with Application in Environmental Studies

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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. (en)
Title	Smooth Estimates of Distribution Functions with Application in Environmental Studies Smooth Estimates of Distribution Functions with Application in Environmental Studies (en)
skos:prefLabel	Smooth Estimates of Distribution Functions with Application in Environmental Studies Smooth Estimates of Distribution Functions with Application in Environmental Studies (en)
skos:notation	RIV/00216224:14310/07:00022321!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(LC06024)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Koláček, Jan Zelinka, Jiří Horová, Ivanka
http://linked.open.../riv/druhVysledku	O - Ostatní výsledky nezařaditelné do žádného z výše uvedených druhů výsledku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	450547
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/07:00022321
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	cumulative distribution function; kernel smoothing; reflection method (en)
http://linked.open.../riv/klicoveSlovo	reflection method kernel smoothing cumulative distribution function
http://linked.open...ontrolniKodProRIV	[65DB00B6CD79]
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Jaroslav Hájek Center for Theoretical and Applied Statistics
http://linked.open...UplatneniVysledku	2007
http://linked.open...iv/tvurceVysledku	Koláček, Jan Horová, Ivanka Zelinka, Jiří El-Shaarawi, Abdel H.
http://localhost/t...ganizacniJednotka	14310

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