×

The moment of maximum normed sums of randomly weighted pairwise NQD sequences. (English) Zbl 1391.60056

Summary: This paper investigates the moment of maximum normed sums of randomly weighted pairwise negative quadrant dependent (NQD) random variables. A sufficient condition to the moment of this stochastic process is obtained, which extends the existing results.

MSC:

60F15 Strong limit theorems
60F25 \(L^p\)-limit theorems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. A DLER, A. R OSALSKY, Some general strong laws for weighted sums of stochastically dominated random variables, Stoch. Anal. Appl. 5 (1987), 1-16. · Zbl 0617.60028
[2] A. A DLER, A. R OSALSKY, R. L. T AYLOR, Strong laws of large numbers for weighted sums of random elements in normed linear spaces, Int. J. Math. Math. Sci. 12 (1989), 507-530. · Zbl 0679.60009
[3] P. Y. C HEN, S. X. G AN, On moments of the maximum of normed partial sums ofρ-mixing random variables, Statist. Probab. Lett. 78 (2008), 1215-1221. · Zbl 1163.60006
[4] P. Y. C HEN, S. H. S UNG, Generalized Marcinkiewicz-Zygmund type inequalities for random vari- ables and applications, J. Math. Inequal. 10 (2016), 837-848. · Zbl 1351.60027
[5] P. Y. C HEN, S. H. S UNG, A Bernstein type inequality for NOD random variables and applications, J. Math. Inequal. 11 (2017), 455-467. · Zbl 1369.60014
[6] X. D ENG, X. J. W ANG, Y. W U, Y. D ING, Complete moment convergence and complete convergence for weighted sums of NSD random variables, RACSAM 110 (2016), 97-120. · Zbl 1334.60037
[7] X. D ENG, X. J. W ANG, F. X. X IA, Hajek-Renyi-type inequality and strong law of large numbers for END sequences, Comm. Statist. Theory Methods 46 (2017), 672-682. · Zbl 1381.60059
[8] S. X. G AN, P. Y. C HEN, Some limit theorems for sequences of pairwise NQD random variables, Acta. Math. Sci. Ser B Engl. 28 (2008), 269-281. · Zbl 1174.60330
[9] D. L. H ANSON, F. T. W RIGHT, A bound on tail probabilities for quadratic forms in independent random variables, Ann. Math. Statist. 42 (1971), 1079-1083. · Zbl 0216.22203
[10] T.-C. H U, C. Y. C HIANG, R. L. T AYLOR, On complete convergence for arrays of rowwise m- negatively associated random variables, Nonlinear Anal. 71 (2009), e1075-e1081. · Zbl 1238.60041
[11] K. J OAG-D EV, F. P ROSCHAN, Negative association of random variables with applications, Ann. Statist. 11 (1983), 286-295. · Zbl 0508.62041
[12] M. H. K O, Complete convergences for arrays of row-wise PNQD random variables, Stoch.: Int. J. Probab. Stoch. Process. 85 (2013), 172-180. · Zbl 1321.60058
[13] E. L. L EHMANN, Some concepts of dependence, Ann. Math. Statist. 37 (1966), 1137-1153. · Zbl 0146.40601
[14] X. Q. L I, Z. R. Z HAO, W. Z. Y ANG, S. H. H U, The inequalities of randomly weighted sums of pairwise NQD sequences and its application to limit theory, J. Math. Inequal. 11 (2017), 323-334. · Zbl 1369.60018
[15] P. M ATULA, A note on the almost sure convergence of sums of negatively dependent random variables, Stat. Probab. Lett. 15 (1992), 209-213. · Zbl 0925.60024
[16] A. T. S HEN, Y. Z HANG, A. V OLODIN, On the strong convergence and complete convergence for pairwise NQD random variables, Abstr. Appl. Anal. 2014 (2014), Article ID 893906, 7 pages. · Zbl 1474.60082
[17] S. H. S UNG, Strong limit theorems for Pairwise NQD random variables, Comm. Statist. Theory Meth ods 42 (2013), 3965-3973. · Zbl 1281.60031
[18] S. H. S UNG, Convergence in r -mean of weighted sums of NQD random variables, Appl. Math. Lett. 26 (2013), 18-24. · Zbl 1256.60016
[19] X. J. W ANG, X. D ENG, L. L. Z HENG, S. H. H U, Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications, Statistics, 48 (2014), 834- 850. · Zbl 1319.60063
[20] X. J. W ANG, T.-C. H U, A. V OLODIN, S. H. H U, Complete convergence for weighted sums and arrays of rowwise extended negatively dependent random variables, Comm. Statist. Theory Methods 42 (2013), 2391-2401. · Zbl 1276.60036
[21] X. J. W ANG, L. X. L I, S. H. H U, X. H. W ANG, On complete convergence for an extended negatively dependent sequence, Comm. Statist. Theory Methods 43 (2014), 2923-2937. · Zbl 1300.60038
[22] X. J. W ANG, C. X U, T.-C. H U, A. V OLODIN, S. H. H U, On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models, Test 23 (2014), 607-629. · Zbl 1307.60024
[23] Y. B. W ANG, J. G. Y AN, F. Y. C HENG, X. Z. C AI, On the strong stability for Jamison type weighted product sums of pairwise NQD series with different distribution, Chin. Ann. Math. 22A (2011), 701- 706. · Zbl 0993.60031
[24] F. T. W RIGHT, A bound on tail probabilities for quadratic forms in independent random variables whose distributions are not necessarily symmetric, Ann. Probab. 1 (1973), 1068-1070. · Zbl 0271.60033
[25] Q. Y. W U, Convergence properties of pairwise NQD random sequences, Acta Math. Sin. Chin. Ser. 45 (2002), 617-624. · Zbl 1008.60039
[26] Q. Y. W U, Complete convergence for negatively dependent sequences of random variables, J. Inequal. Appl. 2010 (2010), Article ID 507293, 10 pages. · Zbl 1202.60050
[27] Q. Y. W U, Almost sure central limit theorem for self-normalized products of partial sums of negatively associated sequences, Comm. Statist. Theory Methods 46 (2017), 2593-2606. · Zbl 1362.60022
[28] Q. Y. W U, Y. Y. J IANG, The strong law of large numbers for pairwise NQD random variables, J. Syst. Sci. Complex. 24 (2011), 347-357. · Zbl 1227.60039
[29] Y. F. W U, G. J. S HEN, On convergence for sequences of pairwise negatively quadrant dependent random variables, Appl. Math. 59 (2014), 473-487. · Zbl 1340.60046
[30] Y. F. W U, M. L. G UO, Convergence of weighted sums for sequences of pairwise NQD random vari- ables, Comm. Statist. Theory Methods, 45 (2016), 5977-5989. · Zbl 1348.60050
[31] C. X U, M. M. X I, X. J. W ANG, H. X IA, Lrconvergence for weighted sums of extended negatively dependent random variables, J. Math. Inequal. 10 (2016), 1157-1167. · Zbl 1356.60057
[32] W. G. Y ANG, D. Y. Z HU, R. G AO, Almost everywhere convergence for sequences of pairwise NQD random variables, Comm. Statist. Theory Methods, 46 (2017), 2494-2505. · Zbl 1364.60038
[33] W. Z. Y ANG, S. H. H U, Complete moment convergence of pairwise NQD random variables, Stoch.: Int. J. Probab. Stoch. Process. 87 (2015), 199-208. · Zbl 1320.60086
[34] M. Y AO, L. L IN, The moment of maximum normed randomly weighted sums of martingale differences, J. Inequal. Appl. 2015, 2015:264. (Received February 5, 2017)Dong Zhao Department of Basic Science Huaibei Vocational and Technical College Huaibei, 235000, China e-mail:zhaodong1973@aliyun.com Xiaoqin Li School of Mathematical Sciences Anhui University Hefei 230601, China e-mail:lixiaoqin1983@163.com Kehan Wu Training Center of Anhui Provincial Eletric Power Company Hefei, 230000, China e-mail:wukehan@yeah.net Journal of Mathematical Inequalities www.ele-math.com
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.