Minimum Distance Density Estimates of a Probability Density on the Real Line

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00209065" target="_blank" >RIV/68407700:21340/13:00209065 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21240/13:00209065

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Minimum Distance Density Estimates of a Probability Density on the Real Line

Popis výsledku v původním jazyce

This paper focuses on the minimum distance density estimate f_n of probability density f on a real line. The rate of consistency of Kolmogorov density estimate for n tending to infinity is known if the degree of variations is finite. The rate of consistency is studied under more general conditions. For this purpose, the generalization of degree of variation - the partial degree of variation is defined for density g of nonparametric family D containing the unknown density f. If the partial degree of variation is finite and some additional, but not as restrictive as a finiteness of degree of variation, assumptions are fulfilled then the Kolmogorov density estimate is consistent with the order n to the -1/2 in L1-norm and also in the expected L1-norm. A small generalization of previous theory is made. Furthermore, some other minimum distance density estimates are explored. (Namely Lévy, discrepanci, and Cramer-von Mises distance.) And with the aid of inequalities between statistical dista

Název v anglickém jazyce

Minimum Distance Density Estimates of a Probability Density on the Real Line

Popis výsledku anglicky

This paper focuses on the minimum distance density estimate f_n of probability density f on a real line. The rate of consistency of Kolmogorov density estimate for n tending to infinity is known if the degree of variations is finite. The rate of consistency is studied under more general conditions. For this purpose, the generalization of degree of variation - the partial degree of variation is defined for density g of nonparametric family D containing the unknown density f. If the partial degree of variation is finite and some additional, but not as restrictive as a finiteness of degree of variation, assumptions are fulfilled then the Kolmogorov density estimate is consistent with the order n to the -1/2 in L1-norm and also in the expected L1-norm. A small generalization of previous theory is made. Furthermore, some other minimum distance density estimates are explored. (Namely Lévy, discrepanci, and Cramer-von Mises distance.) And with the aid of inequalities between statistical dista

Druh

C - Kapitola v odborné knize

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

<a href="/cs/project/LG12020" target="_blank" >LG12020: Využití pokročilé statistické analýzy a nestatistických separačních metod pro detekování fyzikálních procesů v datech snímaných urychlovači elementárních částic.</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Essays on Mathematics and Statistics: Volume 3

ISBN

978-960-9549-34-9

Počet stran výsledku

11

Strana od-do

97-107

Počet stran knihy

308

Název nakladatele

Athens Institute for Education and Research

Místo vydání

Athens

Kód UT WoS kapitoly

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