A random CLT for dependent random variables

Ikuo Sugiman

Journal of Multivariate Analysis, 1986, vol. 20, issue 2, 321-326

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.

Keywords: random; limit; theorem; Anscombe; condition; dependent; random; variables (search for similar items in EconPapers)
Date: 1986
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