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A random CLT for dependent random variables

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  • Sugiman, Ikuo

Abstract

We introduce a new condition for {Y[tau]n} to have the same asymptotic distribution that {Yn} has, where {Yn} is a sequence of random elements of a metric space (S, d) and {[tau]n} is a sequence of random indices. The condition on {Yn} is that maxi[set membership, variant]Dnd(Yi, Yan)-->p0 as n --> [infinity], where Dn = {i: ki-kan [delta]an) --> 0 as n --> [infinity]. Under these conditions, we will show that d(Y[tau]n, Yan) --> P0 and apply this result to the CLT for a general class of sequences of dependent random variables.

Suggested Citation

  • Sugiman, Ikuo, 1986. "A random CLT for dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 321-326, December.
    • Handle: RePEc:eee:jmvana:v:20:y:1986:i:2:p:321-326
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