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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Bibliographic Details
Published in:Acta mathematica Sinica. English series Vol. 40; no. 4; pp. 1127 - 1142
Main Authors: Wu, Yi, Wang, Xue Jun
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024
Springer Nature B.V
Subjects:
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)
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
ISSN:1439-8516, 1439-7617
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-023-1364-y