Uniform Integrability in Anscombe’s Theorem for Martingales

A. Irle
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A. Irle: Mathematisches Seminar der Universität

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 201-207 from Springer

Abstract: 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.

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_14

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DOI: 10.1007/978-94-009-3963-9_14

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