Abstract
I was tremendously privileged to have been one of Wassily Hoeffding’s colleagues. While his demeanor and utter clarity of thought could be intimidating at times, it truthfully can be stated that he was always gracious and generous in his assessments of his colleagues, reserving for himself standards that only someone of his exceptional intellectual stature could hope to achieve.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. W. Anderson (1960), “A modification of sequential analysis to reduce the sample size”, Ann. Math. Statist. 31, 165–197.
Robert Bechhofer, Jack Kiefer, and Milton Sobel (1968), Sequential Identification and Ranking Procedures, Univ. of Chicago Press, Chicago.
Jacques Bernard and Gérard Letac (1973), “Construction d’évenements équiprobables et coefficients multinomiaux modulo p”, Illinois J. Math. 17, 317–332.
David Blackwell and M.A. Girshick (1954), Theory of Games and Statistical Decisions, Wiley, New York.
Manuel Blum (1986), “Independent unbiased coin flips from a correlated biased source — a finite state Markov chain”, Combinatorica 6, 97–108.
Paul Camion (1974), “Unbiased die rolling with a biased die”, produced as a visitor to the University of North Carolina in the Institute of Statistics Mimeo Series No. 920 (unpublished).
Thomas Donnelly (1957), “A family of sequential tests”, unpublished Ph.D. dissertation, University of North Carolina.
Meyer Dwass (1972), “Unbiased coin tossing with discrete random variables”, Ann. Math. Statist. 43, 860–864.
Peter Elias (1972), “The efficient construction of an unbiased random sequence”, Ann. Math. Statist. 43, 865–870.
Wassily Hoeffding (1953), “A lower bound for the average sample number of a sequential test”, Ann. Math. Statist. 24, 127–130.
Wassily Hoeffding (1960a), “Lower bounds for the expected sample size and the average risk of a sequential procedure”, Ann. Math. Statist. 31, 352–368.
Wassily Hoeffding (1960b) “Lower bounds for the expected sample size of a sequential test”, Information and Decision Processes, edited by R.E. Machol, 53–61, McGraw-Hill, New York.
Wassily Hoeffding and Gordon Simons (1970), “Unbiased coin tossing with a biased coin”, Ann. Math. Statist. 41, 341–352.
Jack Kiefer and Lionel Weiss (1957), “Some properties generalized sequential probability ratio tests”, Ann. Math. Statist. 28, 57–74.
Tze Leung Lai (1988), “Nearly optimal sequential tests of composite hypotheses”, Ann. Statist. 16, 856–886.
T.L. Lai, Robbins and Siegmund (1983) “Sequential design of comparative clinical trials”, Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday, Ed. Rizvi, Rustagi, and Siegmund, 51–68, Academic Press, New York.
James Lechner (1972), “Efficient techniques for unbiasing a Bernoulli generator” J. Res. Nat. Bur. Stand. 76B, 53–60.
Gary Lorden (1967), “Integrated risk of asymptotically Bayes sequential tests”, Ann. Math. Statist. 38, 1399–1422.
Gary Lorden (1976), “2-SPRT’s and the modified Kiefer-Weiss problem of minimizing an expected sample size”, Ann. Statist. 4, 281–291.
Paul Samuelson (1968), “Constructing an unbiased random sequence”, J. Am. Statist. Assoc. 63, 1526–1527.
M. P. Schützenberger (1961), “On a special class of recurrent events”, Ann. Math. Statist., 32, 1201–1213.
David Siegmund (1985), Sequential Analysis, Tests and Confidence Intervals, Springer Series in Statistics, Springer-Verlag, New York.
Gordon Simons (1967), “Lower bounds for average sample number of sequential multihypothesis tests”, Ann. Math. Statist. 38, 1343–1364.
Gordon Simons (1976), “An improved statement of optimality for the sequential probability ratio test”, Ann. Statist. 4, 1240–1243.
Quentin Stout and Bette Warren (1984), “Tree algorithms for unbiased coin tossing with a biased coin”, Ann. Prob. 12, 212–222.
John von Neumann (1951), “Various techniques used in connection with random digits”, Monte Carlo Method, Applied Mathematics Series, No. 12, 36–38, U.S. National Bureau of Standards, Washington D.C.
Abraham Wald (1950), Statistical Decision Functions, Wiley, New York.
Abraham Wald and Jacob Wolfowitz (1950), “Bayes solutions of sequential decision problems”, Ann. Math. Statist. 21, 82–99.
Abraham Wald and Jacob Wolfowitz (1948), “Optimum character of the sequential probability ratio test”, Ann. Math. Statist. 18, 326–339.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Simons, G. (1994). The Impact of Wassily Hoeffding’s Work on Sequential Analysis. In: Fisher, N.I., Sen, P.K. (eds) The Collected Works of Wassily Hoeffding. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0865-5_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0865-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6926-7
Online ISBN: 978-1-4612-0865-5
eBook Packages: Springer Book Archive