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Wald's equation and asymptotic bias of randomly stopped  -statistics
Author(s):
Victor
H.
de la Peña;
Tze
Leung
Lai
Journal:
Proc. Amer. Math. Soc.
125
(1997),
917-925.
MSC (1991):
Primary 60G40, 62L12;
Secondary 62L10
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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:
10.1090/S0002-9939-97-03574-0
PII:
S 0002-9939(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
Copyright of article:
Copyright
1997,
American Mathematical Society
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