Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes

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Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes. / Chebunin, M. G.; Kovalevskii, A. P.

In: Siberian Electronic Mathematical Reports, Vol. 20, No. 2, 2023, p. 913-922.

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

BibTeX

@article{3a0d4992a18b4d398ba4e6730e9cf14f,

title = "Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes",

abstract = "We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak convergence to a two-dimensional Gaussian process. Its covariance function depends only on exponent of regular decrease of probabilities. We obtain parameter estimates that have a normal asymototics for its joint distribution together with forward and backward processes. We use these estimates to construct statistical tests for the homogeneity of the urn scheme on the number of thrown balls.",

keywords = "Gaussian process, Zipf's law, statistical test, weak convergence",

author = "Chebunin, {M. G.} and Kovalevskii, {A. P.}",

note = "The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation.",

year = "2023",

doi = "10.33048/semi.2023.20.055",

language = "English",

volume = "20",

pages = "913--922",

journal = "Сибирские электронные математические известия",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

number = "2",

}

RIS

TY - JOUR

T1 - Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes

AU - Chebunin, M. G.

AU - Kovalevskii, A. P.

N1 - The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2023

Y1 - 2023

N2 - We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak convergence to a two-dimensional Gaussian process. Its covariance function depends only on exponent of regular decrease of probabilities. We obtain parameter estimates that have a normal asymototics for its joint distribution together with forward and backward processes. We use these estimates to construct statistical tests for the homogeneity of the urn scheme on the number of thrown balls.

AB - We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak convergence to a two-dimensional Gaussian process. Its covariance function depends only on exponent of regular decrease of probabilities. We obtain parameter estimates that have a normal asymototics for its joint distribution together with forward and backward processes. We use these estimates to construct statistical tests for the homogeneity of the urn scheme on the number of thrown balls.

KW - Gaussian process

KW - Zipf's law

KW - statistical test

KW - weak convergence

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85177554186&origin=inward&txGid=b5063a593ced75bafb0123ffa7f55958

UR - https://www.mendeley.com/catalogue/77460603-5ec1-3324-9e80-0301e3b56b6f/

U2 - 10.33048/semi.2023.20.055

DO - 10.33048/semi.2023.20.055

M3 - Article

VL - 20

SP - 913

EP - 922

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

ER -

ID: 59241671