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A renewal theorem and its applications to some sequential procedures. (English) Zbl 0496.62067


MSC:

62L12 Sequential estimation
60G40 Stopping times; optimal stopping problems; gambling theory

Citations:

Zbl 0354.62065
Full Text: DOI

References:

[1] Anscombe, F. J., Large sample theory of sequential estimation, Proc. Cambridge Philos. Soc., 48, 600-607 (1952) · Zbl 0047.13401
[2] Chow, Y. S.; Studden, W., Monotonicity of the variance under truncation and variations of Jensen’s inequality, Ann. Math. Statist., 40, 1106-1108 (1969) · Zbl 0204.53102
[3] Chow, Y. S.; Teicher, H., Probability Theory (1978), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0399.60001
[4] Chow, Y. S.; Yu, K. F., The performance of a sequential procedure for the estimation of the mean, Ann. Statist., 9, 184-189 (1981) · Zbl 0452.62070
[5] Gut, A., On the moments and limit distributions of some first passage times, Ann. Probability, 2, 277-308 (1974) · Zbl 0278.60031
[6] Lai, T. L.; Siegmund, D., A nonlinear renewal theory with applications to sequential analysis I, Ann. Statist., 5, 946-954 (1977) · Zbl 0378.62069
[7] Lai, T. L.; Siegmund, D., A nonlinear renewal theory with applications to sequential analysis II, Ann. Statist., 7, 60-76 (1979) · Zbl 0409.62074
[8] Robbins, H., Sequential estimation of the mean of a normal population. Probability and Statistics (Harald Cramer Volume) (1959), Upsala: Almquist and Wiksell, Upsala · Zbl 0095.13005
[9] Robbins, H.; Siegmund, D.; Williams, E. J., Sequential estimation ofp in Bernoulli trials. Studies in Probability and Statistics (1974), Melbourne: University of Melbourne, Melbourne
[10] Siegmund, D., Some one-sided stopping rules, Ann. Math. Statist., 38, 1641-1646 (1967) · Zbl 0183.20707
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