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http://dx.doi.org/10.5351/CKSS.2012.19.2.247

On Complete Convergence for Weighted Sums of Pairwise Negatively Quadrant Dependent Sequences  

Ko, Mi-Hwa (Division of Mathematics and Informational Statistics, WonKwang University)
Publication Information
Communications for Statistical Applications and Methods / v.19, no.2, 2012 , pp. 247-256 More about this Journal
Abstract
In this paper we prove the complete convergence for weighted sums of pairwise negatively quadrant dependent random variables. Some results on identically distributed and negatively associated setting of Liang and Su (1999) are generalized and extended to the pairwise negative quadrant dependence case.
Keywords
Negative quadrant dependence; complete convergence; weighted sums; negative association;
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1 Kafles, D. and Bhaskara Rao, M. (1982). Weak consistency of least squares estimators in linear models, Journal of Multivariate Analysis, 12, 186-198.   DOI
2 Kuczmaszewska, A. (2009). On complete convergence for arrays of rowwise negatively associated random variables, Statistics and Probability Letters, 79, 116-124.   DOI   ScienceOn
3 Lehmann, E. L. (1966). Some concepts of dependence, Annals of Mathematical Statistics, 37, 1137-1153.   DOI
4 Li, D. L., Rao, M. B., Jiang, T. F. and Wang, X. C. (1995). Complete convergence and almost sure convergence of weighted sums of random variables, Journal of Theoretical Probability, 8, 49-76.   DOI
5 Liang, H. Y. (2000). Complete convergence for weighted sums of negatively associated random variables, Statistics and Probability Letters, 48, 317-325.   DOI   ScienceOn
6 Liang, H. Y. and Su, C. (1999). Complete convergence for weighted sums of NA sequences, Statistics and Probability Letters, 45, 85-95.   DOI   ScienceOn
7 Rao, C. R. and Zhao, M. T. (1992). Linear representation of M-estimates in linear models, Canadian Journal of Statistics, 20, 359-368.   DOI
8 Tolley, H. D. and Norman, J. E. (1979). Time on trial estimates with bivariate risk, Biometrika, 66, 285-291.   DOI   ScienceOn
9 Wu, Q. (2006). Probability Limit Theory for Mixing Sequences, Science Press, Beijing, China, 170-176, 206-211.
10 Bai, Z. and Su, C. (1985). The complete convergence for partial sums of i.i.d. random variables, Science China Mathematics, A28, 1261-1277
11 Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing Probability Models, Holt, Rinehart and Winston, New York.
12 Cheng, P. E. (1995). A note on strong convergence rates in nonparametric regression, Statistics and Probability Letters, 24, 357-364.   DOI   ScienceOn
13 Gut, A. (1992). Complete convergence for arrays, Periodica Mathematica Hungarica, 25, 51-75.   DOI
14 Gut, A. (1993). Complete convergence and Cesaro summation for i.i.d. random variables, Probability Theory and Related Fields, 97, 169-178.   DOI
15 Hsu, P. L. and Robbins, H. (1947). Complete convergence and the law of large numbers, Proceedings of the National Academy of Sciences of the United States of America, 33, 25-31.
16 Joag-Dev, K. and Proschan, F. (1983). Negative association of random variables with applications, Annals of Statistics, 11, 286-295.   DOI
17 Johnson, N. L. and Kotz, S. (1972). Distributions in Statistics: Continuous Multivariate Distributions, Wiley, New York.