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Convergence rates in the law of large numbers for i.i.d. random variables have been generalized by Gut[Gut, A., 1978. Marc inkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6, 469-482] to random fields with all indices having the same power in the normalization. In this paper we generalize these convergence rates to the identically distributed and negatively associated random fields with different indices having different power in the normalization.
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참고문헌 (7)
참고문헌 신청
Gut, A / Marcinkiewicz laws and convergence rates in the law of large num- bers for random variables with multidimensional indices / Ann Probab 6:469~482
Gut, A. / 2009 / An asymmetric Marcinkiewicz - Zygmund LLN for random fields / Statist. Probab. Lett 79:1016~1020
Hsu, P.L. / 1947 / Complete convergence and the law of large numbers / Proc. Nat. Acad. Sci. U.S.A 33:25~31
Joag-Dev, K / 1983 / Negative association of random variables with applications / Ann. Statist 11:286~295
Li, G / 1994 / Multidimensional Levy inequalities and their applications / Probab. Lett 20:327~335
Gut, A. / 2009 / An asymmetric Marcinkiewicz - Zygmund LLN for random fields / Statist. Probab. Lett 79:1016~1020
Hsu, P.L. / 1947 / Complete convergence and the law of large numbers / Proc. Nat. Acad. Sci. U.S.A 33:25~31
Joag-Dev, K / 1983 / Negative association of random variables with applications / Ann. Statist 11:286~295
Li, G / 1994 / Multidimensional Levy inequalities and their applications / Probab. Lett 20:327~335
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