The Collected Works of Wassily Hoeffding

It has been a rare privilege to assemble this volume of Wassily Hoeffding's Collected Works. Wassily was, variously, a teacher, supervisor and colleague to us, and his work has had a profound influence on our own. Yet this would not be sufficient reason to publish his collected works. The additional and overwhelmingly compelling justification comes from the fun­ damental nature of his contributions to Statistics and Probability. Not only were his ideas original, and far-reaching in their implications; Wassily de­ veloped them so completely and elegantly in his papers that they are still cited as prime references up to half a century later. However, three of his earliest papers are cited rarely, if ever. These include material from his doctoral dissertation. They were written in German, and two of them were published in relatively obscure series. Rather than reprint the original articles, we have chosen to have them translated into English. These trans­ lations appear in this book, making Wassily's earliest research available to a wide audience for the first time. All other articles (including those of his contributions to Mathematical Reviews which go beyond a simple reporting of contents of articles) have been reproduced as they appeared, together with annotations and corrections made by Wassily on some private copies of his papers. Preceding these articles are three review papers which dis­ cuss the . impact of his work in some of the areas where he made major contributions.

Contenu

Three Articles Reviewing Hoeffding's Work.- Wassily Hoeffding' s Work in the Sixties.- The Impact of Wassily Hoeffding's Work on Sequential Analysis.- The Impact of Wassily Hoeffding's Research on Nonparametrics.- Publications.- Scale-Invariant Correlation Theory (English Translation).- Scale-Invariant Correlations for Discontinuous Distributions (English Translation).- Stochastic Dependence and Functional Relationships (English Translation).- On the Distribution of the Rank Correlation Coefficient r when the Variates are not Independent.- A Class of Statistics with Asymptotically Normal Distribution.- The Central Limit Theorem for Dependent Random Variables (with Herbert Robbins).- A Non-Parametric Test of Independence.- 'Optimum' Non-Parametric Tests.- A Combinatorial Central Limit Theorem.- The Large-Sample Power of Tests Based on Permutations of Observations.- On the Distribution of the Expected Values of the Order Statistics.- A Lower Bound for the Average Sample Number of a Sequential Test.- Bounds for the Distribution of a Sum of Independent, Identically Distributed Random Variables (with S.S. Shrikhande).- The Efficiency of Tests (with J.R. Rosenblatt).- The Extrema of the Expected Value of a Function of Independent Random Variables.- On the Distribution of the Number of Successes in Independent Trials.- The role of Assumptions in Statistical Decisions.- Distinguishability of Sets of Distributions. (The case of Independent and Identically Distributed Random Variables) (with J Wolfowitz).- Lower Bounds for the Expected Sample Size and the Average Risk of a Sequential Procedure.- An Upper Bound for the Variance of Kendall's 'Tau' and of Related Statistics.- Lower Bounds for the Expected Sample Size of a Sequential Test.- On Sequences of Sums of Independent Random Vectors.- Probability Inequalities for Sums of Bounded Random Variables.- On a Theorem of V.M. Zolotarev.- Asymptotically Optimal Tests for Multinomial Distributions (with Discussion).- On Probabilities of Large Deviations.- Some Recent Developments in Nonparametric Statistics.- Unbiased Coin Tossing with a Biased Coin (with Gordon Simons).- Discussion of J. Hájek, Miscellaneous Problems of Rank Test Theory.- Discussion of H. Witting, On the Theory of Nonparametric Tests.- The L1 norm of the Approximation Error for Bernstein-Type Polynomials.- On the Centering of a Simple Linear Rank Statistic.- The L1 norm of the Approximation Error for Splines with Equidistant Knots.- Harold Hotelling, 1895-1973.- H.Hotelling.- Some Incomplete and Boundedly Complete Families of Distributions.- More on Incomplete and Boundedly Complete Families of Distributions.- A Statistician's Progress from Berlin to Chapel Hill.- Unbiased Range-Preserving Estimators.- Range Preserving Unbiased Estimators in the Multinomial Case.- Entries in The Encyclopedia of Statistical Sciences edited by S. Kotz, N.L. Johnson and C.B. Read. New York: Wiley.- Asymptotic Normality.- Hájek's Projection Lemma.- Hoeffding's Independence Test.- Probability Inequalities for Sums of Bounded Random Variables.- Range-Preserving Estimators.- Book Reviews.- S.S. Wilks, Mathematical Statistics.- G. Udny Yule Sz M. G. Kendall, An Introduction to the Theory of Statistics, 14th Edition.- D.A.S. Fraser, Nonparametric Methods in Statistics.- B.V. Gnedenko & A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables.- J. Hájek & S. sidak, Theory of Rank Tests.- E.L. Lehmann, Testing Statistical Hypotheses.