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Maximal inequalities for averages of i.i.d. and 2-exchangeable random variables

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  • Etemadi, N.

Abstract

Let {X,Xn: n[greater-or-equal, slanted]1} be a sequence of 2-exchangeable random variables, i.e., any two random variables in the sequence have the same joint probability distribution function as any other two. Any sequence of random variables in which the random variables are either i.i.d., or pairwise independent, identically distributed, or exchangeable is also 2-exchangeable. Let . We will obtain upper and lower bounds for the distribution function of max1[less-than-or-equals, slant]i[less-than-or-equals, slant]n Si/i. For i.i.d. real valued random variables our result translates into,for every positive integer n and [lambda]>0.

Suggested Citation

  • Etemadi, N., 1999. "Maximal inequalities for averages of i.i.d. and 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 195-200, August.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:2:p:195-200
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    References listed on IDEAS

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    1. Etemadi, N., 1997. "Criteria for the strong law of large numbers for sequences of arbitrary random vectors," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 151-157, April.
    2. Qiying, Wang, 1996. "On the maximal inequality," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 85-89, December.
    3. Etemadi, N. & Kaminski, M., 1996. "Strong law of large numbers for 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 245-250, July.
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