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Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 211–233 (Mi znsl6551)  

This article is cited in 1 scientific paper (total in 1 paper)

Exact $L_2$-small ball asymptotics for some Durbin processes

Yu. P. Petrova

St. Petersburg State University, Mathematics and Mechanics Faculty, St. Petersburg, Russia

Abstract: We find the exact $L_2$-small ball asymptotics for some Durbin processes. These processes are finite dimentional perturbations of the Brownian bridge $B(t)$ and naturally appear in statistics as limit ones when building goodness-of-fit tests of $\omega^2$-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 was developed. Due to this, it is possible to calculate the asymptotics of small deviations for Durbin processes for certain distributions (Laplace, logistic, Gumbel, gamma).

Key words and phrases: spectral asymptotics, Gaussian processes, small deviations.

Funding Agency Grant Number
Russian Science Foundation 17-11-01003
Russian Foundation for Basic Research 16-01-00258


Full text: PDF file (281 kB)
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Document Type: Article
UDC: 519.2
Received: 23.11.2017

Citation: Yu. P. Petrova, “Exact $L_2$-small ball asymptotics for some Durbin processes”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 211–233

Citation in format AMSBIB
\Bibitem{Pet17}
\by Yu.~P.~Petrova
\paper Exact $L_2$-small ball asymptotics for some Durbin processes
\inbook Probability and statistics. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 466
\pages 211--233
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6551}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Petrova Yu.P., “On Spectral Asymptotics For a Family of Finite-Dimensional Perturbations of Operators of Trace Class”, Dokl. Math., 98:1 (2018), 367–369  crossref  zmath  isi  scopus
  • Записки научных семинаров ПОМИ
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