# Wassily Hoeffding

### Quick Info

Mustamäki, Finland (now Mukhino, Russia)

Chapel Hill, North Carolina, USA

**Wassily Hoeffding**was a Finnish statistician and probability theorist.

### Biography

**Wassily Hoeffding**'s parents lived in Tsarskoye Selo (meaning the Tsar's Village, and now named Pushkin) which is 22 kilometres south of St Petersburg. However, they spent the summer in Mustamäki, at that time part of the Russian Empire, and it was there that Wassily was born. He gives some details of his family in [2]:-

My father, whose parents were Danish, was an economist and a disciple of Peter Struve, the Russian social scientist and public figure. An uncle of my father's was Harald Hoeffding, the philosopher. My mother, née Wedensky, had studied medicine. Both grandfathers had been engineers.Wassily was one of his parents' three sons, having an older brother Waldemar and a younger brother Oleg. He spent the first six years of his life in Tsarskoye Selo - well that is not quite accurate since the city was renamed Detskoe Selo (meaning the Children's Village) in 1918. He did not begin schooling in Russia, but after the family moved to Denmark in 1920 he entered elementary school. They only spent four years in Denmark before they moved again, this time settling in Berlin.

Hoeffding attended an Oberrealschule in Berlin where he received a good training in natural sciences and languages. His favourite subject was mathematics but, perhaps rather surprisingly, he disliked physics. With no strong views as to the career he would like to follow when he graduated from the Oberrealschule in 1933, he decided that it would be sensible for him to follow in his father's footsteps and become an economist. Therefore, in 1933, he entered the Handelshochschule (now called the Wirtschaftshochschule) in Berlin. However, he quickly discovered that economics was not the right choice for him [2]:-

But I soon found that economics was too vague a science for me. Chance phenomena and their laws captured my interest. I performed series of random tossings and recorded their outcomes before I knew much about probability theory. One of the few books on chance phenomena that I found in the library of the Hochschule was 'Die Analyse des Zufalls' Ⓣ by H E Timerding, and it fascinated me. In 1934 I entered Berlin University to study mathematicsOn 30 January 1933 the National Socialist party led by Hitler had come to power in Germany. Hitler, as Chancellor of Germany, immediately announced legal action against Germany's Jews. On 7 April 1933 the Nazis introduced a law for the "Restoration of the civil service" which dismissed all non-Aryans and Jewish civil servants from their positions with the exception of those who either had fought in the Great War or had been in office since August 1914. Although these laws did not affect Hoeffding personally, they had a major consequence on his education at the University of Berlin. Part of these consequences was that Richard von Mises, who was a leading expert on probability theory, had left the University of Berlin. Von Mises would have kept his position under the exemption clauses but he correctly realised that this would not save him for long and had left Germany. The other consequence of the "Restoration of the civil service" as far as Hoeffding was concerned was the difficult atmosphere that resulted around the university with some inferior academics gaining high positions because of their strong support for the Nazis.

The only course in mathematical statistics given at the University of Berlin at this time was by Alfred Klose. He had been a disciple of von Mises and taught the course keeping closely to a textbook written by von Mises. Hoeffding took this course but also studied, among other, advanced calculus with Erhard Schmidt and number theory with Alfred Brauer (whom he considered the best of all his lecturers). He continued working towards his doctorate [2]:-

My Doktorvater or Ph.D. supervisor was Klose. I chose the topic of the thesis and worked on it largely by myself, with some suggestions and encouragement from him. He was a Baltic German and had his own ideas about Russians. He warned me to refrain from making exaggerated claims in my thesis that I could not substantiate as, he thought, Russians were prone to do.For his doctorate Hoeffding studied properties of bivariate distributions which are invariant under certain transformations. He submitted his thesis

*Maszstabinvariante Korrelationstheorie*Ⓣ to the University of Berlin in 1940 and was awarded his doctorate. Of course, by this time Germany was at war but Hoeffding was not liable to be called up at this time since he was not a German citizen. In fact he was stateless, since he lost his Russian citizenship when leaving in 1920 and did not wish to take German citizenship. However, making a career in Germany during World War II was pretty nearly impossible but Hoeffding managed to obtain two part-time jobs. One of these was as an editorial assistant with the reviewing journal

*Jahrbuchs über die Fortschritte der Mathematik*Ⓣ while the other was as a research assistant with the Berliner Hochschulinstitut für Versicherungswissenschaft, an institute for actuarial science.

He was still holding these two part-time posts in 1944 when stateless persons were called up for military service if they were of 'German or related blood'. The Danish name Hoeffding was sufficient to qualify under the 'related blood' clause but when he went for a medical it was realised that he suffered from diabetes so he was excused military service in the army. Harald Geppert, the editor of the

*Jahrbuch*, suggested that Hoeffding should work on mathematics with military applications and so that he be seen to be contributing towards the war effort. However, Hoeffding told him that his conscience would not allow him to contribute to the Nazi cause - a very dangerous statement to make in Nazi Germany, particularly to Geppert who was sympathetic to the Nazi cause.

In February 1945 Hoeffding and his mother left Berlin. The final acts of the war were taking place with the Russians approaching from the east and, after taking Posnan by the end of January, they were advancing towards Dresden. On 3 February 1945, 1000 bombers, supported by 900 fighters, attacked Berlin causing massive damage. Hoeffding and his parents were fortunate to escape with their lives in these bombing raids but the irony was that Hoeffding's brother Oleg spent the war working for the Economic Division of the U.S. Embassy in England and was involved in the planning of this devastating raid which almost killed his family. Of course, the Hoeffding family in Berlin only realised the involvement of Oleg in planning the raid much later. Hoeffding and his mother went to a small town in Hanover where a Swiss friend of the family were living. Hoeffding's father remained in Berlin and was captured by the Russians when Berlin fell. Since Hoeffding's father had worked as an economist for the American Commercial Attaché, the Russians treated him as a spy and he was imprisoned.

The British troops took Hanover and after the surrender of Germany it came under British control. Hoeffding remained there for over a year while he tried to have his father released - they did not succeed. While living there Hoeffding and his mother were visited by Oleg, wearing American uniform. Hoeffding asked his brother to send him Maurice Kendall's

*The Advanced Theory of Statistics*. He read it avidly and it led to his first statistics paper

*The distribution of the rank correlation coefficient t when the variates are not independent*. Although written in Hanover in 1946, by the time of its publication in 1947, Hoeffding was in the United States. By the summer of 1946 Hoeffding had no idea where his father was being held prisoner (he was actually being held in Potsdam and would eventually escape) so, with his mother, he left Germany for Switzerland. After a long trip across Europe, they sailed for New York, arriving in September 1946.

Arriving in New York without any prospect of a job, Hoeffding attended statistics lectures at Columbia University. In particular he attended lectures by Abraham Wald and by his collaborator Jacob Wolfowitz, both on the Faculty at Columbia. He also attended a course given by Jerzy Neyman who was at that time on the Faculty of the University of California at Berkeley but was visiting Columbia University. Hoeffding had gone to New York to join his brother Oleg who had been appointed as an Instructor in Economics at Columbia University in the summer of 1946. Oleg was able to get his brother invitations to visit the Cowles Commission for Economic Research at Chicago University and the Department of Mathematical Statistics at the University of North Carolina. He went first to Chicago but while there, received an offer from Harold Hotelling at the University of North Carolina, Chapel Hill, of the post of research associate there. This offer was made without any visit or interview taking place, simply on the merits of Hoeffding's doctoral thesis. Despite a rival offer from Chicago, he accepted Hotelling's offer and arrived in Chapel Hill to take up his new position in May 1947. Hoeffding spent the rest of his career at Chapel Hill.

While Hoeffding was in Chicago, he had given a talk on his latest work on U-statistics (the U stands for 'unbiased estimator') and he published this highly significant idea in the paper

*A class of statistics with asymptotically normal distribution*(1948). A mark of the importance of this paper is that it was partially reprinted in the 1992 book

*Breakthroughs in Statistics*. This was not the only paper Hoeffding published in 1948 for another two of his papers appeared that year, namely

*A non-parametric test of independence*, and (with his colleague Herbert Robbins)

*The central limit theorem for dependent random variables*. The book [1] of his

*Collected Works*:-

... consists of forty papers, six book reviews and five contributions to the Encyclopedia of Statistical Science ... His early papers (three of them) originally published in German, have been translated into English. Also, there are three articles reviewing (i) Hoeffding's work during the sixties, the impact of his work on (ii) sequential analysis, and (iii) on nonparametric inference.Hoeffding's methods of teaching and examining students is certainly worth recording [6]:-

As with all other aspects of his professional life, Wassily approached his interactions with students with very careful thought. In his later years in the department his teaching was confined to advanced graduate courses, of which he taught five: Estimation and Hypothesis Testing, Nonparametric Statistics, Sequential Analysis, Decision Theory, and Large-Sample Theory. For this level of student the courses were a delight: as elegantly and meticulously prepared as his research papers, always totally up-to-date, and above all designed to promote understanding and learning. Furthermore, his examinations were a revelation. He had the view that students taking his courses wanted to learn, and that it wasn't his job to seek to catch them out by probing for areas of confusion or lack of knowledge. Rather, his examinations, which took the form of one-week take-home projects, simply extended the learning process, by leading the student through an area of the subject not covered in the course.In 1973 he was appointed Kenan Professor at the University of North Carolina and, six years later, in 1979, he retired. To celebrate his 65th birthday in 1979 an Advanced International Symposium was organised at Chapel Hill. He relates in [2] unfortunate events that took place:-

Unfortunately, in the middle of the symposium banquet, I had to leave for the hospital, where my right leg had to be amputated. (The reason was an infection related to my diabetes.)Despite these problems, Hoeffding lived for another twelve years. He died of pneumonia at Haven Hill Nursing Home in Chapel Hill.

It is clear that Hoeffding's remarkable contributions to statistics would result in him receiving the highest honours. These honours include being invited to be Wald Lecturer (1967) and president of the Institute of Mathematical Statistics (1969). He was elected to the National Academy of Sciences (1976), the American Academy of Arts and Sciences (1985); the American Statistical Association; the Institute of Mathematical Statistics; and the International Statistical Institute. He was elected an Honorary Fellow of the Royal Statistical Society.

After he retired the University of North Carolina's College of Arts and Sciences honoured him by establishing the Wassily Hoeffding Professorship.

Let us end this biography by quoting from the tribute from Herbert Robbins at Hoeffding's funeral:-

Although he was gentle and courteous in manner and fragile in health, he was lion-hearted in spirit and completely original in his scientific work. His character was truly noble; I never heard from him a complaint about his chronic illness or the difficulties of living in an alien environment, or a disparaging remark about any fellow human being.

### References (show)

- N I Fisher and P K Sen (eds.),
*The Collected Works of Wassily Hoeffding*(Springer, New York, 1994). - J Gani (ed),
*The Making of Statisticians*(Springer-Verlag, New York, 1982). - I M Chakravarti, Biographical sketch : Wassily Hoeffding, in
*Asymptotic theory of statistical tests and estimation, Proc. Adv. Internat. Sympos., Univ. North Carolina, Chapel Hill, N.C., 1979*(Academic Press, New York-London-Toronto, Ont., 1980), xi-xiv. - E Fels, Review: Russian-English Dictionary of Statistical Terms and Expressions and Russian Reader in Statistics by Samuel Kotz with the collaboration of Wassily Hoeffding,
*Econometrica***33**(3) (1965), 659-660. - N I Fisher and W R van Zwet, Wassily Hoeffding : June 12, 1914-February 28, 1991,
*Biographical Memoirs National Academy***86**(2005), 209-224. - N I Fisher and W R van Zwet, Remembering Wassily Hoeffding,
*Statist. Sci.***23**(4) (2008), 536-547. - R F Rinehart, Review: Russian-English Dictionary of Statistical Terms and Expressions and Russian Reader in Statistics by Samuel Kotz with the collaboration of Wassily Hoeffding,
*Operations Research***13**(1) (1965), 163-164. - Wassily Hoeffding, 76, Authority on Statistics,
*New York Times*(3 March 1991).

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update March 2011

Last Update March 2011