Exact L 2-Small Ball Asymptotics for Some Durbin Processes

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Exact L ₂-Small Ball Asymptotics for Some Durbin Processes. / Petrova, Yu P.

In: Journal of Mathematical Sciences , Vol. 244, No. 5, 01.02.2020, p. 842-857.

Research output: Contribution to journal › Article › peer-review

Author

Petrova, Yu P. / Exact L ₂-Small Ball Asymptotics for Some Durbin Processes. In: Journal of Mathematical Sciences . 2020 ; Vol. 244, No. 5. pp. 842-857.

BibTeX

@article{f58950ab553944ef8d71d34f9d47b120,

title = "Exact L 2-Small Ball Asymptotics for Some Durbin Processes",

abstract = "We find the exact L2-small ball asymptotics for some Durbin processes. These processes are finitedimensional perturbations of a Brownian bridge B(t) and naturally appear in statistics as limit ones when one constructs goodness-of-fit tests of ω2-type for testing a sample for some distribution with estimated parameters. Earlier, in the work of Nazarov and Petrova, Kac–Kiefer–Wolfowitz processes (which correspond for testing normality) were considered, where a technique for obtaining asymptotics of oscillating integrals with a slowly varying amplitude has been developed. Due to this, it is possible to calculate the asymptotics of small deviations for Durbin processes for certain distributions (Laplace, logistic, Gumbel, gamma).",

author = "Petrova, {Yu P.}",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2020",

month = feb,

day = "1",

doi = "10.1007/s10958-020-04657-9",

language = "English",

volume = "244",

pages = "842--857",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Exact L 2-Small Ball Asymptotics for Some Durbin Processes

AU - Petrova, Yu P.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - We find the exact L2-small ball asymptotics for some Durbin processes. These processes are finitedimensional perturbations of a Brownian bridge B(t) and naturally appear in statistics as limit ones when one constructs goodness-of-fit tests of ω2-type for testing a sample for some distribution with estimated parameters. Earlier, in the work of Nazarov and Petrova, Kac–Kiefer–Wolfowitz processes (which correspond for testing normality) were considered, where a technique for obtaining asymptotics of oscillating integrals with a slowly varying amplitude has been developed. Due to this, it is possible to calculate the asymptotics of small deviations for Durbin processes for certain distributions (Laplace, logistic, Gumbel, gamma).

AB - We find the exact L2-small ball asymptotics for some Durbin processes. These processes are finitedimensional perturbations of a Brownian bridge B(t) and naturally appear in statistics as limit ones when one constructs goodness-of-fit tests of ω2-type for testing a sample for some distribution with estimated parameters. Earlier, in the work of Nazarov and Petrova, Kac–Kiefer–Wolfowitz processes (which correspond for testing normality) were considered, where a technique for obtaining asymptotics of oscillating integrals with a slowly varying amplitude has been developed. Due to this, it is possible to calculate the asymptotics of small deviations for Durbin processes for certain distributions (Laplace, logistic, Gumbel, gamma).

UR - http://www.scopus.com/inward/record.url?scp=85077704359&partnerID=8YFLogxK

U2 - 10.1007/s10958-020-04657-9

DO - 10.1007/s10958-020-04657-9

M3 - Article

VL - 244

SP - 842

EP - 857

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 78547875