Optimal Choice of Nonparametric Estimates of a Density and of its Derivatives
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F02%3A00007553" target="_blank" >RIV/00216224:14310/02:00007553 - isvavai.cz</a>
Výsledek na webu
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DOI - Digital Object Identifier
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Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Optimal Choice of Nonparametric Estimates of a Density and of its Derivatives
Popis výsledku v původním jazyce
Kernel smoothers are one of the most popular nonparametric functional estimates. These smoothers depend on three parameters: the bandwidth which controls the smoothness of the estimate, the form of the kernel weight function and the order of the kernel which is related to the number of derivatives assumed to exist in the nonparametric model. Because these three problems are closely related one to each other it is necessary to address them all together. In this paper we concentrate on the estimation of adensity function and of its derivatives. We propose to use polynomial kernels and we construct data-driven choices for the bandwidth and the order of the kernel. We show a~theorem stating that this method for solving simultaneously the three selection problems mentioned before is asymptotically optimal in terms of Mean Integrated Squared Errors. As a by-product of our result we show an asymptotic optimality property for a~new bandwidth selector for density derivative which is quite appe
Název v anglickém jazyce
Optimal Choice of Nonparametric Estimates of a Density and of its Derivatives
Popis výsledku anglicky
Kernel smoothers are one of the most popular nonparametric functional estimates. These smoothers depend on three parameters: the bandwidth which controls the smoothness of the estimate, the form of the kernel weight function and the order of the kernel which is related to the number of derivatives assumed to exist in the nonparametric model. Because these three problems are closely related one to each other it is necessary to address them all together. In this paper we concentrate on the estimation of adensity function and of its derivatives. We propose to use polynomial kernels and we construct data-driven choices for the bandwidth and the order of the kernel. We show a~theorem stating that this method for solving simultaneously the three selection problems mentioned before is asymptotically optimal in terms of Mean Integrated Squared Errors. As a by-product of our result we show an asymptotic optimality property for a~new bandwidth selector for density derivative which is quite appe
Klasifikace
Druh
J<sub>x</sub> - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
CEP obor
BA - Obecná matematika
OECD FORD obor
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Návaznosti výsledku
Projekt
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Návaznosti
Z - Vyzkumny zamer (s odkazem do CEZ)
Ostatní
Rok uplatnění
2002
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Statistics & Decisions
ISSN
0721-2631
e-ISSN
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Svazek periodika
20
Číslo periodika v rámci svazku
4
Stát vydavatele periodika
DE - Spolková republika Německo
Počet stran výsledku
24
Strana od-do
355-378
Kód UT WoS článku
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EID výsledku v databázi Scopus
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