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Diskr. Mat., 2016, Volume 28, Issue 3, Pages 49–58 (Mi dm1383)  

Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process

A. M. Zubkova, M. P. Savelovb

a Steklov Mathematical Institute of Russian Academy of Sciences
b Lomonosov Moscow State University

Abstract: It is shown that, with suitable time change, the finite-dimensional distributions of the process formed by successive values of the Pearson statistics for an expanding sample converge to finite-dimensional distributions of the stationary random process, namely, the normalized square of the Bessel process. The results obtained earlier on the limit joint distributions of the Pearson statistics are used to derive explicit formulas for the density of joint distributions of the Bessel process.

Keywords: Pearson statictics, sequential chi-square test, Bessel process

DOI: https://doi.org/10.4213/dm1383

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English version:
Discrete Mathematics and Applications, 2017, 27:6, 405–411

Bibliographic databases:

Document Type: Article
UDC: 519.214.5
Received: 24.06.2016

Citation: A. M. Zubkov, M. P. Savelov, “Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process”, Diskr. Mat., 28:3 (2016), 49–58; Discrete Math. Appl., 27:6 (2017), 405–411

Citation in format AMSBIB
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