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Journal of Theoretical Probability

, Volume 13, Issue 2, pp 343–356 | Cite as

A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables

  • Qi-Man Shao
Article

Abstract

Let {Xi, 1≤in} be a negatively associated sequence, and let {X* i , 1≤in} be a sequence of independent random variables such that X* i and Xi have the same distribution for each i=1, 2,..., n. It is shown in this paper that Ef(∑ n i=1Xi)≤Ef(∑ n i=1X* i ) for any convex function f on R1 and that Ef(max1≤kn n i=kXi)≤Ef(max1≤kn k i=1X* i ) for any increasing convex function. Hence, most of the well-known inequalities, such as the Rosenthal maximal inequality and the Kolmogorov exponential inequality, remain true for negatively associated random variables. In particular, the comparison theorem on moment inequalities between negatively associated and independent random variables extends the Hoeffding inequality on the probability bounds for the sum of a random sample without replacement from a finite population.

negative dependence independent random variables comparison theorem moment inequality 

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Qi-Man Shao
    • 1
  1. 1.Department of MathematicsUniversity of OregonEugene

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