Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors
Let be an array of martingale difference random vectors and be an array of m × d matrices of real numbers. In this paper, the Marcinkiewicz–Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p -th (1 < p...
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| Published in: | Acta mathematica Sinica. English series Vol. 40; no. 4; pp. 1127 - 1142 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2024
Springer Nature B.V |
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| ISSN: | 1439-8516, 1439-7617 |
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| Abstract | Let
be an array of
martingale difference random vectors and
be an array of
m
×
d
matrices of real numbers. In this paper, the Marcinkiewicz–Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite
p
-th (1 <
p
< 2) moments. Moreover, the complete convergence and strong law of large numbers are established under some mild conditions. An application to multivariate simple linear regression model is also provided. |
|---|---|
| AbstractList | Let
be an array of
martingale difference random vectors and
be an array of
m
×
d
matrices of real numbers. In this paper, the Marcinkiewicz–Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite
p
-th (1 <
p
< 2) moments. Moreover, the complete convergence and strong law of large numbers are established under some mild conditions. An application to multivariate simple linear regression model is also provided. Let be an array of martingale difference random vectors and be an array of m × d matrices of real numbers. In this paper, the Marcinkiewicz–Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th (1 < p < 2) moments. Moreover, the complete convergence and strong law of large numbers are established under some mild conditions. An application to multivariate simple linear regression model is also provided. |
| Author | Wu, Yi Wang, Xue Jun |
| Author_xml | – sequence: 1 givenname: Yi surname: Wu fullname: Wu, Yi organization: School of Big Data and Artificial Intelligence, Chizhou University – sequence: 2 givenname: Xue Jun surname: Wang fullname: Wang, Xue Jun email: wxjahdx@126.com organization: School of Big Data and Statistics, Anhui University |
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| Cites_doi | 10.1023/A:1021744626773 10.1016/j.spl.2015.11.017 10.1007/s10474-014-0424-2 10.1007/s10474-010-9091-0 10.1016/S0167-9473(03)00088-4 10.1073/pnas.33.2.25 10.1007/s10474-018-0865-0 10.1214/aoms/1177730037 10.1016/j.spl.2018.02.068 10.1016/j.scient.2012.09.010 10.1007/s10474-009-9166-y 10.1007/s11749-017-0550-6 10.1016/0167-9473(90)90001-X 10.1090/S0002-9947-1965-0198524-1 10.1080/02331888.2021.1909028 10.1007/s10474-015-0516-7 10.1007/s10114-013-2243-8 10.1080/07362998708809104 10.1016/j.jmaa.2014.05.067 10.1186/s13660-018-1710-2 10.1186/s13660-017-1566-x 10.1155/2010/630608 |
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| Keywords | weighted sums complete convergence Martingale difference random vectors Marcinkiewicz–Zygmund type weak law of large numbers 60G50 strong law of large numbers multivariate simple linear regression model 60F15 |
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| Snippet | Let
be an array of
martingale difference random vectors and
be an array of
m
×
d
matrices of real numbers. In this paper, the Marcinkiewicz–Zygmund type weak... Let be an array of martingale difference random vectors and be an array of m × d matrices of real numbers. In this paper, the Marcinkiewicz–Zygmund type weak... |
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| SubjectTerms | Arrays Big Data Codes Convergence Inequality Martingales Mathematical analysis Mathematics Mathematics and Statistics Multivariate analysis Random variables Real numbers Regression analysis Regression models Sums Vectors (mathematics) |
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| Title | Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors |
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