Previous |  Up |  Next

Article

Keywords:
complete convergence; complete moment convergence; $L^q$ convergence; pairwise NQD random variables
Summary:
In this paper the authors study the convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables. The results extend and improve the corresponding theorems of T. C. Hu, R. L. Taylor: On the strong law for arrays and for the bootstrap mean and variance, Int. J. Math. Math. Sci 20 (1997), 375–382.
References:
[1] Adler, A., Rosalsky, A., Volodin, A.: A mean convergence theorem and weak law for arrays of random elements in martingale type $p$ Banach spaces. Stat. Probab. Lett. 32 (1997), 167-174. DOI 10.1016/S0167-7152(97)85593-9 | MR 1436862 | Zbl 0874.60008
[2] Bryc, W., Smoleński, W.: Moment conditions for almost sure convergence of weakly correlated random variables. Proc. Am. Math. Soc. 119 (1993), 629-635. DOI 10.1090/S0002-9939-1993-1149969-7 | MR 1149969 | Zbl 0785.60018
[3] Chow, Y. S.: On the rate of moment complete convergence of sample sums and extremes. Bull. Inst. Math. Acad. Sin. 16 (1988), 177-201. MR 1089491
[4] Ebrahimi, N., Ghosh, M.: Multivariate negative dependence. Commun. Stat., Theory Methods 10 (1981), 307-337. DOI 10.1080/03610928108828041 | MR 0612400 | Zbl 0506.62034
[5] Gan, S. X., Chen, P. Y.: On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables. Acta Math. Sci., Ser. B, Engl. Ed. 27 (2007), 283-290. DOI 10.1016/S0252-9602(07)60027-7 | MR 2313226 | Zbl 1125.60027
[6] Hsu, P. L., Robbins, H.: Complete convergence and the law of large numbers. Proc. Natl. Acad. Sci. 33 (1947), 25-31. DOI 10.1073/pnas.33.2.25 | MR 0019852 | Zbl 0030.20101
[7] Hu, T. C., Taylor, R. L.: On the strong law for arrays and for the bootstrap mean and variance. Int. J. Math. Math. Sci. 20 (1997), 375-382. DOI 10.1155/S0161171297000483 | MR 1444739 | Zbl 0883.60024
[8] Joag-Dev, K., Proschan, F.: Negative association of random variables with applications. Ann. Stat. 11 (1983), 286-295. DOI 10.1214/aos/1176346079 | MR 0684886
[9] Lehmann, E. L.: Some concepts of dependence. Ann. Math. Stat. 37 (1966), 1137-1153. DOI 10.1214/aoms/1177699260 | MR 0202228 | Zbl 0146.40601
[10] Wang, D. C., Zhao, W.: Moment complete convergence for sums of a sequence of NA random variables. Appl. Math., Ser. A (Chin. Ed.) 21 (2006), 445-450 Chinese. MR 2270685 | Zbl 1137.60320
[11] Wu, Q. Y.: Convergence properties of pairwise NQD random sequences. Acta Math. Sin. 45 (2002), 617-624 Chinese. MR 1915127 | Zbl 1008.60039
[12] Wu, Y. F., Zhu, D. J.: Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables. J. Korean Stat. Soc. 39 (2010), 189-197 \MR 2642485. DOI 10.1016/j.jkss.2009.05.003 | MR 2642485 | Zbl 1294.60056
[13] Yang, S. C.: Almost sure convergence of weighted sums of mixing sequences. J. Syst. Sci. Math. Sci. 15 (1995), 254-265 Chinese. Zbl 0869.60029
Partner of
EuDML logo