Wald’s equation and asymptotic bias of randomly stopped $U$-statistics
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- by Victor H. de la Peña and Tze Leung Lai PDF
- Proc. Amer. Math. Soc. 125 (1997), 917-925 Request permission
Abstract:
In this paper we make use of decoupling arguments and martingale inequalities to extend Wald’s equation for sample sums to randomly stopped de-normalized $U$-statistics. We also apply this result in conjunction with nonlinear renewal theory to obtain asymptotic expansions for the means of normalized $U$-statistics from sequential samples.References
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Additional Information
- Victor H. de la Peña
- Affiliation: Department of Statistics, Columbia University, 617 Mathematics Bldg., New York, New York 10027
- MR Author ID: 268889
- Email: vp@wald.stat.columbia.edu
- Tze Leung Lai
- Affiliation: Department of Statistics, Stanford University, Sequoia Hall, Stanford, California 94305-4065
- Email: karola@playfair.stanford.edu
- Received by editor(s): October 15, 1994
- Received by editor(s) in revised form: July 28, 1995
- Additional Notes: The first author’s research was supported by the National Science Foundation under DMS-9310682.
The second author’s research was supported by the National Science Foundation under DMS-9403794. - Communicated by: Wei Y. Loh
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 917-925
- MSC (1991): Primary 60G40, 62L12; Secondary 62L10
- DOI: https://doi.org/10.1090/S0002-9939-97-03574-0
- MathSciNet review: 1350937