Wald's equation and asymptotic bias

of randomly stopped -statistics

Authors:
Victor H. de la Peña and Tze Leung Lai

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

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Abstract | References | Similar Articles | Additional Information

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 -statistics. We also apply this result in conjunction with nonlinear renewal theory to obtain asymptotic expansions for the means of normalized -statistics from sequential samples.

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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

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

DOI:
https://doi.org/10.1090/S0002-9939-97-03574-0

Keywords:
Hoeffding decomposition,
decoupling,
martingales,
Wald's equation,
stopping times

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

Article copyright:
© Copyright 1997
American Mathematical Society