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Jacob Wolfowitz

Born: 19 March 1910 in Warsaw, Russian Empire (now Poland)
Died: 16 July 1981 in Tampa, Florida, USA

Jacob Wolfowitz's father emigrated to the USA in 1914 and Jacob joined
him in 1920 when he was ten years old. Jacob attended High School in
New York and, having graduated, entered the College of the City of New
York. While Wolfowitz was in the middle of his undergraduate course
the Great Depression began.

The Great Depression began in 1929 and by 1932 one quarter of the
workers in the United States were unemployed. When Wolfowitz graduated
in 1931 there was little prospects of good employment so he spent the
next ten years teaching mathematics in a number of different high
schools while he worked towards his doctorate. In 1934 Wolfowitz
married Lillian Dundes; they had one daughter, born in 1941 and a son
Paul, born in 1943. Paul Wolfowitz became the Deputy Secretary of
Defense (sic) for the USA in March 2001.

Wolfowitz met Wald in 1938 and they began a collaboration which lasted
until Wald's death [2]:-

They were the closest of friends, and Wolfowitz regarded Wald as his
teacher as well as his co-worker. Their work together produced some of
the most important and striking results in theoretical statistics.

In fact the first paper which Wolfowitz wrote was a joint one with
Wald. Wolfowitz's earliest interest was nonparametric inference and
the joint paper we just mentioned presents ways of calculating
confidence intervals which are not necessarily of fixed width, on a
distribution function F based on the empiric independent identically
distributed observations on F. It is in a paper by Wolfowitz in 1942
that the word 'nonparametric' appears for the first time.

Wolfowitz obtained his doctorate from New York University in 1942 and
that year joined the Statistical Research Group at Columbia
University. This research group was working on problems related to war
work and one of the statistical methods it was working on was
sequential analysis. The type of problem that this statistical method
applies to is when the number of observations of a variable is not
determined before the experiment begins, but rather the number of
observations is determined by the observations themselves. Wald and
Wolfowitz were both attached to the Statistical Research Group at
Columbia and they led the research project to develop a theory for
sequential analysis. Wolfowitz produced work on sequential estimators
of a Bernoulli parameter, and results on the efficiency of certain
sequential estimators. Again he collaborated with Wald on work in this
area, and one particular result should be mentioned, namely their
proof of the optimal character of the sequential probability ratio
test for testing between two hypotheses. This result is described in
[2] as:-

... one of the strikingly beautiful results of theoretical statistics.

At the end of the war Wolfowitz left the Columbia research group and
took up a position as associate professor at University of North
Carolina. After spending the year 1945-46 there, he returned to
Columbia University. He remained at Columbia until after the death of
Wald, then he was appointed professor of mathematics at Cornell in
1951. While on the Faculty at Cornell he was visiting professor at the
University of California at Los Angeles in 1952, at the University of
Illinois in 1953, Technion in Israel in 1957. In 1967 he was visiting
professor at both Technion and the University of Paris, and he spent a
period at the University of Heidelberg in 1969. He left Cornell and
joined the University of Illinois at Urbana in 1970 , retiring in 1978
when he then went to the University of South Florida at Tampa. In 1979
he was Shannon Lecturer of the Institute of Electrical and Electronic

As someone who collaborated with others frequently on research, it is
worth hearing the opinions of collaborators who [2]:-

... attest to the stimulating experience of doing joint research with
him. In research discussions he is energetic, probing, critical,
humorous, and very inventive.

We have mentioned Wolfowitz's work on nonparametric inference and his
work on sequential analysis. He also studied asymptotic statistical
theory, that is the theory of how statistical processes behave in the
limit as the sample size gets larger and larger. The properties of
consistency and efficiency are important here, the first ensuring
convergence and the second relating to the rate of convergence.
Wolfowitz looked at many aspects of the maximum likelihood method.

Information theory, which had been started by Shannon, was another
area to which Wolfowitz made important contributions. His book Coding
Theorems of Information Theory (3rd ed. 1978) is a classic in the
subject. It is [2]:-

... the only book which concentrates on statistical and probabilistic
aspects of noisy channel communication theory. It is also a handy
introductory text because of its brief and simple formulations of
problems and estimates. Yet it is comprehensive and at the limits of
present research. The completely revised third edition is
indispensable for specialists, as the other two editions were before.
It contains the core of the ideas of Wolfowitz's papers and of
research influenced by him, which already means that the main stream
of present research in this theory is covered.

We should also mention what a fine teacher Wolfowitz was [2]:-

His lectures reflect his own insistence on understanding the essential
features of a proof. "Lets see what makes things tick", his class
hear, and his students and audiences at scientific meetings have the
privilege of receiving a lively and lucid exposition that enables them
to appreciate the crucial ideas of a subject much more than does the
customary formal lecture or line by line proof. ... His students ...
always found generosity, patience, and the deep personal concern along
with helpful criticism.

Wolfowitz received many honours for his outstanding contributions to
statistics. He was elected to the National Academy of Sciences, and
the American Academy of Arts and Sciences. He was elected a Fellow of
the Econometric Society, the International Statistics Institute, and
the Institute of Mathematical Statistics. He was both Rietz Lecturer
and Wald Lecturer for this latter Institute. Technion, in Israel,
awarded him an honorary degree in 1975.

Finally, a comment on his personality and interests outside
mathematics and statistics:-

He is a voracious reader, and his knowledge of, and intense interest
in, all facets of the state of the world, make him an interesting
person with whom to discuss almost anything.

Article by: J J O'Connor and E F Robertson