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ASYMMETRIC COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF MARTINGALE DIFFERENCE FIELDS
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  • Journal title : Honam Mathematical Journal
  • Volume 36, Issue 1,  2014, pp.33-41
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2014.36.1.33
 Title & Authors
ASYMMETRIC COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF MARTINGALE DIFFERENCE FIELDS
Ko, Mi-Hwa;
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 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;
 Language
English
 Cited by
 References
1.
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. crossref(new window)

2.
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.

3.
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.

4.
Gut, A. and Stadtmuller U., An asymmetric Marcinkiewicz-Zygmund SLLN for random fields, Statist. Probab. Letts. 35 (2009), 756-763.

5.
Hsu, P.L. and Robbins, H., Complete convergence and the law of large numbers, Proc. Natl. Acad. Sci. USA 33 (1947), 25-31. crossref(new window)

6.
Joag-Dev, K. and Proschan, F., Negative association of random variables with applications, Ann. Statist. 11 (1983), 286-295. crossref(new window)

7.
Kafles, D. and Bhaskara Rao, M., Weak consistency of least squares estimators in linear models, J. Multivariate Anal. 12 (1982), 186-198. crossref(new window)

8.
Ko, M.H., On complete convergence for weighted sums of martingale-difference random Fields, Journal of Inequalities and Applications 2013:473 (2013). crossref(new window)

9.
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. crossref(new window)

10.
Lehmann, E.L., Some concepts of dependence, Ann. Math. Stat. 37 (1966), 1137-1153. crossref(new window)

11.
Priestley, M.B. and Chao, M.T., Nonparametric function fitting, J. Roy. Statist. Soc. Ser. B 34 (1972), 385-392.

12.
Rao, C.R. and Zhao, L.C., Linear representation of M-estimates in linear models, Canad. J. Statist. 20 (1992), 359-368. crossref(new window)