A Note on Random Sums with Nonrandom Centering

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Let X1, X2,... be a sequence of i.i.d. random variables and Nn a sequence ot nonnegative integer valued random variables, independent of {Xi}. The main results concern tightness and weak convergence of (A1, + ... + XNn-nμ) γn1 under the natural condition that the sample mean is a consistent estimator of μ.

Original languageEnglish (US)
Pages (from-to)333-348
Number of pages16
JournalJournal of Theoretical Probability
Issue number2
StatePublished - 1997


  • Domain of attraction
  • Nonrandom centering
  • Random sum
  • Tightness
  • Weak convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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