Large Deviation Principle for Moderate Deviation Probabilities of Bootstrap Empirical Measures

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Large Deviation Principle for Moderate Deviation Probabilities of Bootstrap Empirical Measures. / Ermakov, M. S.

в: Journal of Mathematical Sciences (United States), Том 204, № 1, 2015, стр. 90-115.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{3c6c1a550328472db0fda2e89a598de3,

title = "Large Deviation Principle for Moderate Deviation Probabilities of Bootstrap Empirical Measures",

abstract = "We prove two Large Deviation Principles (LDP) in the zone of moderate deviation probabilities. First we establish the LDP for conditional distributions of moderate deviations of empirical bootstrap measures given an empirical probability measure. Then we establish the LDP for the joint distributions of an empirical measure and a bootstrap empirical measure. Using these LDPs, similar LDPs for differentiable statistical functionals can be established. The LDPs for moderate deviations of an empirical quantile process and an empirical bootstrap copula function are provided as illustrations of these results. Bibliography: 28 titles.",

author = "Ermakov, {M. S.}",

year = "2015",

doi = "10.1007/s10958-014-2189-0",

language = "English",

volume = "204",

pages = "90--115",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Large Deviation Principle for Moderate Deviation Probabilities of Bootstrap Empirical Measures

AU - Ermakov, M. S.

PY - 2015

Y1 - 2015

N2 - We prove two Large Deviation Principles (LDP) in the zone of moderate deviation probabilities. First we establish the LDP for conditional distributions of moderate deviations of empirical bootstrap measures given an empirical probability measure. Then we establish the LDP for the joint distributions of an empirical measure and a bootstrap empirical measure. Using these LDPs, similar LDPs for differentiable statistical functionals can be established. The LDPs for moderate deviations of an empirical quantile process and an empirical bootstrap copula function are provided as illustrations of these results. Bibliography: 28 titles.

AB - We prove two Large Deviation Principles (LDP) in the zone of moderate deviation probabilities. First we establish the LDP for conditional distributions of moderate deviations of empirical bootstrap measures given an empirical probability measure. Then we establish the LDP for the joint distributions of an empirical measure and a bootstrap empirical measure. Using these LDPs, similar LDPs for differentiable statistical functionals can be established. The LDPs for moderate deviations of an empirical quantile process and an empirical bootstrap copula function are provided as illustrations of these results. Bibliography: 28 titles.

UR - http://www.scopus.com/inward/record.url?scp=84925510949&partnerID=8YFLogxK

U2 - 10.1007/s10958-014-2189-0

DO - 10.1007/s10958-014-2189-0

M3 - Article

AN - SCOPUS:84925510949

VL - 204

SP - 90

EP - 115

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -

ID: 71601827