zbMATH — the first resource for mathematics

Some limit theorems for negatively associated random variables. (English) Zbl 1308.60032
Summary: Let \(\{X_n: n\geq 1\}\) be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems for the negatively associated sequence, which include the \(L^p\)-convergence theorem and the Marcinkiewicz-Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.

60F15 Strong limit theorems
Full Text: DOI
[1] Alam K, Saxena K M L, Positive dependence in multivariate distributions, Comm. Statist. A-Theory Methods10(12) (1981) 1183-1196 · Zbl 0471.62045
[2] Block H W, Savits T H and Shaked M, Some concepts of negative dependence, Ann. Probab.10(3) (1982) 765-772 · Zbl 0501.62037
[3] Jing B Y and Liang H Y, Strong limit theorems for weighted sums of negatively associated random variables, J. Theoret. Probab.21(4) (2008) 890-909 · Zbl 1162.60008
[4] Joag-Dev K and Proschan F, Negative association of random variables, with applications, Ann. Statist.11(1) (1983) 286-295 · Zbl 0508.62041
[5] Matuła P, A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett. 15(3) (1992) 209-213 · Zbl 0925.60024
[6] Newman C M, Asymptotic independence and limit theorems for positively and negatively dependent random variables. Inequalities in statistics and probability (Lincoln, Neb., 1982), IMS Lecture Notes Monogr. Ser., 5, Inst. Math. Statist. (1984) (Hayward, CA) pp. 127-140
[7] Roussas G G, Exponential probability inequalities with some applications. Statistics, probability and game theory, IMS Lecture Notes Monogr. Ser. 30, Inst. Math. Statist. (1996) (Hayward, CA) pp. 303-319
[8] Shao Q M, A comparison theorem on moment inequalities between negatively associated and independent random variables, J. Theoret. Probab.13(2) (2000) 343-356 · Zbl 0971.60015
[9] Shao Q M and Su C, The law of the iterated logarithm for negatively associated random variables, Stochastic Process. Appl.83(1) (1999) 139-148 · Zbl 0997.60023
[10] Su C, Zhao L C and Wang Y B, Moment inequalities and weak convergence for negatively associated sequences, Sci. China Ser. A40(2) (1997) 172-182 · Zbl 0907.60023
[11] Taylor R L, Patterson R F and Bozorgnia A, A strong law of large numbers for arrays of rowwise negatively dependent random variables, Stochastic Anal. Appl.20(3) (2002) 643-656 · Zbl 1003.60032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.