Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Wald’s equation and asymptotic bias of randomly stopped $U$-statistics
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 60G40, 62L12, 62L10
  • Retrieve articles in all journals with MSC (1991): 60G40, 62L12, 62L10
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