Browse > Article
http://dx.doi.org/10.5831/HMJ.2014.36.1.33

ASYMMETRIC COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF MARTINGALE DIFFERENCE FIELDS  

Ko, Mi-Hwa (Division of Mathematics and Informational Statistics, Wonkwang University)
Publication Information
Honam Mathematical Journal / v.36, no.1, 2014 , pp. 33-41 More about this Journal
Abstract
Ko(2013, JIA 2013:473) discussed complete convergence for weighted sum of martingale difference field when all indices have the same powers in the normalization. In this paper we generalize this law to the case where different indices have different powers in the normalization.
Keywords
complete convergence; weighted sums; martingale difference; normalization;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Kafles, D. and Bhaskara Rao, M., Weak consistency of least squares estimators in linear models, J. Multivariate Anal. 12 (1982), 186-198.   DOI
2 Priestley, M.B. and Chao, M.T., Nonparametric function fitting, J. Roy. Statist. Soc. Ser. B 34 (1972), 385-392.
3 Ko, M.H., On complete convergence for weighted sums of martingale-difference random Fields, Journal of Inequalities and Applications 2013:473 (2013).   DOI
4 Kuczmaszewska, A. and Lagodowski, Z., Convergence rates in the SLLN for some classes of dependent random fields, J. Math. Anal. Appl. 380 (2011), 571-584.   DOI
5 Rao, C.R. and Zhao, L.C., Linear representation of M-estimates in linear models, Canad. J. Statist. 20 (1992), 359-368.   DOI
6 Gut, A. and Stadtmuller U., An asymmetric Marcinkiewicz-Zygmund SLLN for random fields, Statist. Probab. Letts. 35 (2009), 756-763.
7 Chen, P. and Hao, C., A remark on the law of the logarithm for weighted sums of random variables with multidimensional indices, Statist. Probab. Letts. 81 (2011), 1808-1812.   DOI
8 Czerebak-Mrozowicz, E.B., Klesov, O.I. and Rychlik, Z., Marcinkiewicz-type strong law of large numbers for pairwise independent random fields, Probab. Math. Statist. 22 (2002), 127-139.
9 Fazekas, I. and Tomacs, T., Strong laws of large numbers for pairwise independent random variables with multidimensional indices, Publ. Math. Debrecen 53 (1998), 149-161.
10 Hsu, P.L. and Robbins, H., Complete convergence and the law of large numbers, Proc. Natl. Acad. Sci. USA 33 (1947), 25-31.   DOI   ScienceOn
11 Joag-Dev, K. and Proschan, F., Negative association of random variables with applications, Ann. Statist. 11 (1983), 286-295.   DOI   ScienceOn
12 Lehmann, E.L., Some concepts of dependence, Ann. Math. Stat. 37 (1966), 1137-1153.   DOI   ScienceOn