Rates of convergence in the operator-stable limit theorem

Makoto Maejima, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Suppose that the ℝd-valued random vector 0 is strictly operator-stable in the sense that μ̂, the characteristic function of 0, satisfies μ̂(z)t = μ̂(tB*z) for every t > 0, for some invertible linear operator B on ℝd. Suppose also that for the i.i.d. random vectors {Xi} in ℝd, n-B Σi=1n Xiw 0. In the present paper, we study the rates of convergence of this operator-stable limit theorem in terms of several probability metrics. A new type of "ideal" metrics suitable for this rate-of-convergence problem is introduced.

Original languageEnglish
Pages (from-to)37-85
Number of pages49
JournalJournal of Theoretical Probability
Volume9
Issue number1
DOIs
StatePublished - Jan 1996

Keywords

  • Operator-stable distributions
  • Probability metrics
  • Rate of convergence

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