Smooth Estimates of Distribution Functions with Application in Environmental Studies
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F07%3A00022321" target="_blank" >RIV/00216224:14310/07:00022321 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Smooth Estimates of Distribution Functions with Application in Environmental Studies
Original language 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 theperformance 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.
Czech name
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Czech description
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Classification
Type
O - Miscellaneous
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/LC06024" target="_blank" >LC06024: Jaroslav Hájek Center for Theoretical and Applied Statistics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů