Probability tail for linearly negative quadrant dependent random variables of partial sums and application to linear model Inequalities for LNQD R.V of partial sums and application

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Zoubeyr Kaddour
Abderrahmane Belguerna
https://orcid.org/0000-0002-1666-1044
Samir Benaissa

Abstract

In this paper, we establish a new concentration inequality and complete convergence of weighted sums for arrays of rowwise linearly negative quadrant dependent (LNQD, in short) random variables and obtain a result dealing with complete convergence of first-order autoregressive processes with identically distributed LNQD innovations.

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How to Cite
[1]
Kaddour, Z. et al. 2022. Probability tail for linearly negative quadrant dependent random variables of partial sums and application to linear model: Inequalities for LNQD R.V of partial sums and application. Journal of Innovative Applied Mathematics and Computational Sciences. 2, 2 (Aug. 2022), 14–22. DOI:https://doi.org/10.58205/jiamcs.v2i2.26.
Section
Conference paper (ICMA'2021)
Author Biographies

Zoubeyr Kaddour

Department of Mathematics and computer sciences, S.A University center of Naâma.

Samir Benaissa

D.L University of SBA

References

P. Erdös, On a theorem of Hsu and Robbins, Ann. Math. Statist., 20(2) (1949), 286–291.

S. Ghosal and T. K. Chandra, Complete convergence of martingale arrays, J. Theo. Probab. 11(3) (1998), 621–631.

A. Gut, Complete convergence for arrays, Period. Math. Hungar. 25 (1992), 51–75.

P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proceedings of the National Academy of Sciences, USA., 33(2) (1947), 25–31.

T. C. Hu, D. Li, A. Rosalsky and A. Volodin, On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements, Theory Probab. Appl., 47(3) (2001), 455–468.

T. C. Hu, A. Rosalsky, D. Szynal and A. Volodin, On complete convergence for arrays of rowwise independent random elements in Banach spaces, Stochastic Anal. Appl., 17(6) (1999), 963–992.

K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist., 11 (1983), 286–295.

T-S. Kim and H-C. Kim, On the exponential inequality for negative dependent sequence, Commun. Korean Math. Soc., 22(2) (2007), 315–321.

M-H. Ko, D-H. Ryu, T-S. Kim and Y-G. Choi , A central limit theorem for general weighted sums of LNQD random variables and its applications, Rocky Mountain J. Math., 37(1) (2007), 259–268.

A. Kuczmaszewska and D. Szynal, On complete convergence in a Banach space, Internat. J. Math. Math. Sci., 17 (1994), 1–14.

E. L. Lehmann, Some concepts of dependence, Ann. Math. Statist., 37(5) (1966), 1137–1153.

C. M. Newman, Asymptotic independence and limit theorems for positively and negatively dependent random variables, Institute of Mathematical Statistics Lecture Notes-Monograph Series, 5 (1984), 127–140.

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