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Uniform Integrability in Anscombe’s Theorem for Martingales

In: Mathematical Statistics and Probability Theory

Author

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  • A. Irle

    (Mathematisches Seminar der Universität)

Abstract

A useful tool in sequential analysis is Anscombe’s theorem. It asserts that asymptotic normality of standardized sums persists when n is replaced by a random index Tn, provided that Tn/n converges in probability to a finite constant. To obtain moment convergence in Anscombe’s theorem one needs uniform integrability results for standardized random sums, and we investigate this question of uniform integrability in the case of martingale differences.

Suggested Citation

  • A. Irle, 1987. "Uniform Integrability in Anscombe’s Theorem for Martingales," Springer Books, in: M. L. Puri & P. Révész & W. Wertz (ed.), Mathematical Statistics and Probability Theory, pages 201-207, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3963-9_14
    DOI: 10.1007/978-94-009-3963-9_14
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