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Teoriya Veroyatnostei i ee Primeneniya, 2024, Volume 69, Issue 4, Pages 760–779
DOI: https://doi.org/10.4213/tvp5643 (Mi tvp5643) 		 
Limiting behaviours for weighted sums of $m$-WOD random variables under integrability assumptions

Wu Y.a, Xi M. M.b, Wang X. J.b

a School of Big Data and Artificial Intelligence, Center of Applied Mathematics, Chizhou University, Chizhou, P. R. China
b School of Big Data and Statistics, Anhui University, Hefei, P. R. China
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DOI: https://doi.org/10.4213/tvp5643
Abstract: In this work, the $L_r$-convergence for weighted sums of $R$-$h$-integrable $m$-WOD random variables, the complete convergence, complete moment convergence, and complete $f$-moment convergence for weighted sums of $SR$-$h$-integrable $m$-WOD random variables are established, which improve and generalize some previously obtained results in the literature. As an application, the weak consistency of the wavelet estimator in nonparametric regression models is obtained under very general assumptions.
Keywords: $L_r$-convergence, complete convergence, complete moment convergence, complete $f$-moment convergence, weighted sum, $R$-$h$-integrability, $SR$-$h$-integrability, $m$-WOD random {variable}.
Funding agency Grant number
National Social Science Foundation of China 22BTJ059
National Natural Science Foundation of China 12201079
12201600
12471248
Natural Science Foundation of Anhui Province 2308085MA07
Postdoctoral Science Foundation of China 2022M713056
Supported by the National Social Science Foundation of China (22BTJ059), the National Natural Science Foundation of China (12201079, 12201600, 12471248), the Natural Science Foundation of Anhui Province (2308085MA07), and the Postdoctoral Science Foundation of China (2022M713056).
Received: 07.03.2023
Published: 25.10.2024
English version:
Theory of Probability and its Applications, 2025, Volume 69, Issue 4, Pages 605–621
DOI: https://doi.org/10.1137/S0040585X97T992161
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Wu Y., Xi M. M., Wang X. J., “Limiting behaviours for weighted sums of $m$-WOD random variables under integrability assumptions”, Teor. Veroyatnost. i Primenen., 69:4 (2024), 760–779; Theory Probab. Appl., 69:4 (2025), 605–621
Citation in format AMSBIB
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\by Wu~Y., Xi~M.~M., Wang~X.~J.
\paper Limiting behaviours for weighted sums of $m$-WOD random variables under integrability assumptions
\jour Teor. Veroyatnost. i Primenen.
\yr 2024
\vol 69
\issue 4
\pages 760--779
\mathnet{http://mi.mathnet.ru/tvp5643}
\crossref{https://doi.org/10.4213/tvp5643}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4914729}
\transl
\jour Theory Probab. Appl.
\yr 2025
\vol 69
\issue 4
\pages 605--621
\crossref{https://doi.org/10.1137/S0040585X97T992161}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-86000066027}
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