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In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.
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참고문헌 (28)
참고문헌 신청
백종일 / 2009 / Almost Sure Convergence for Asymptotically Almost Negatively Associated Random Variable Sequences / Communications for Statistical Applications and Methods 16(6):1013~1022
Jong-Il Baek / 2008 / On the complete convergence of weighted sums for arrays of negatively associated variables / Journal of the Korean Statistical Society 37(1):73~80
GUANG-HUI CAI / 2008 / COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF SEQUENCES OF AANA RANDOM VARIABLES / Glasgow Mathematical Journal 50(3):351~357
Tapas K. Chandra / 1996 / The strong law of large numbers for weighted averages under dependence assumptions / Journal of Theoretical Probability 9(3):797~809
T. K. Chandra / 1996 / Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables / Acta Mathematica Hungarica 71(4):327~336
Jong-Il Baek / 2008 / On the complete convergence of weighted sums for arrays of negatively associated variables / Journal of the Korean Statistical Society 37(1):73~80
GUANG-HUI CAI / 2008 / COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF SEQUENCES OF AANA RANDOM VARIABLES / Glasgow Mathematical Journal 50(3):351~357
Tapas K. Chandra / 1996 / The strong law of large numbers for weighted averages under dependence assumptions / Journal of Theoretical Probability 9(3):797~809
T. K. Chandra / 1996 / Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables / Acta Mathematica Hungarica 71(4):327~336
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