STATISTICIANS IN HISTORY
Jack Wolfowitz: Applying
Mathematical Statistics to
Practical Problems
This is an excerpt from Jack Wolfowitz’s memoriam,
which was written by Lionel Weiss and published in
The American Statistician in 1981.
J
ack (Jacob) Wolfowitz was born in Warsaw,
Poland, on March 19, 1910, and came to the
United States with his family in 1920. He graduated from the College of the City of New York in
1931 and worked toward his PhD while supporting
himself as a high-school teacher. He earned his PhD
in mathematics from New York University in 1942.
In 1934, Wolfowitz married Lillian Dundes,
who he remained committed to in marriage for the
rest of his life.
In 1938, Abraham Wald came to Columbia
University; it was then that Wolfowitz and he
started their remarkable collaboration. Their first
joint paper, “Confidence Limits for Continuous
Distributions,” was published in the Annals of
Mathematical Statistics in 1939. Wolfowitz revered
Wald, and after Wald was killed in a plane crash
in 1950, a large photograph of Wald occupied a
prominent place on Wolfowitz’s office wall.
During World War II, Wald and Wolfowitz
worked together on war-related research at the
Statistical Research Group at Columbia University.
In 1945, Wolfowitz became an associate professor at
The University of North Carolina at Chapel Hill. In
1946, he joined the faculty at Columbia University,
where he stayed until 1951. In 1951, he joined the
department of mathematics at Cornell University.
In 1970, he joined the department of mathematics
at the University of Illinois at Urbana-Champaign.
When he retired from the last position in 1978, he
became distinguished professor at the University of
SEPTEMBER 2010 Amstat News
15
South Florida at Tampa, a position he held until he
died on July 16, 1981.
As a teacher, Wolfowitz was unmatched in his
ability to explain the intuition underlying the most
complicated research results. His own drive toward
intuitive understanding led him to many interesting results. An outstanding example of this was his
investigation of why the maximum likelihood estimator works as well as it does in so many cases,
an investigation that started in 1949 with “On
Wald’s Proof of the Consistency of the Maximum
Likelihood Estimate,” published in the Annals of
Mathematical Statistics, and continued for most of
the rest of his life.
It is interesting that during this investigation,
Wolfowitz and Jack Kiefer found what seems to be
the first example of a case that might arise in practice in which the method of maximum likelihood
breaks down: It is the program of estimating µ and
σ based on n iid observations, each with
which is discussed in “Consistency of the Maximum
Likelihood Estimator in the Presence of Infinitely
Many Incidental Parameters,” published in 1956 in
Annals of Mathematical Statistics.
Wolfowitz’s research touched every important
area of mathematical statistics and extended outside
of mathematical statistics into such fields as probability theory, inventory theory, and coding theory. In this last field, he is considered as eminent a
researcher as he is in mathematical statistics. A good
account of his research, as well as a complete bibliography, can be found in Jacob Wolfowitz: Selected
Papers, edited by Kiefer and published by Springer
in 1980.
Most of Wolfowitz’s publications are highly
mathematical, but much of his research has direct
practical application. An example is the sequence of
papers on the inventory problem, written with Aryeh
(Arie) Dvoretzky and Kiefer, which appeared in
Econometrica in April 1952, July 1952, and October
1953. These were pioneering papers in what is now
a whole field of study; operations research departments give full courses in inventory theory.
Wolfowitz also felt strongly that the ultimate justification for research in mathematical statistics is
its applicability to practical problems. In this connection, his 1967 paper, “Remarks on the Theory
of Testing Hypotheses,” published in the New York
Statistician, is particularly interesting. A few excerpts
will illustrate the outlook expressed in this paper:
“I have written of the divorcement from reality
of much of current research in mathematical
statistics.”
16
Amstat News SEPTEMBER 2010
“The practical statisticians who now accept
useless theory should rebel and not do so any
more.”
“What about the mathematical statisticians,
especially the talented and mathematically
productive among them? Most of the papers
they write on testing hypotheses are, at their
best, mathematically ingenious and difficult,
of no general mathematical interest, and no
lasting statistical importance.”
It is significant that Wolfowitz chose this nontechnical article to be included in the volume of
selected papers.
Wolfowitz’s research contains many asymptotic results. His attitude toward asymptotic theory
was that it was merely a guide to the choice of
appropriate statistical decision rules for moderate
sample sizes, necessary because computations that
are impractical for finite sample sizes often become
relatively easy as sample sizes increase. Large-scale
computer simulation is just becoming economically feasible, which will make it possible to evaluate statistical decision rules for small and moderate
sample sizes. I think Wolfowitz would welcome
such Monte Carlo investigations.
His honors include an honorary doctorate from
the Technion in 1975, election to the National
Academy of Sciences and American Academy of
Arts and Sciences, and becoming a Fellow of the
ASA, Econometric Society, International Statistical
Institute, and Institute of Mathematical Statistics.
He served a term as president of the Institute of
Mathematical Statistics and was chosen as Rietz
Lecturer and Wald Lecturer. In 1979, he was the
Shannon Lecturer of the Institute of Electrical and
Electronic Engineers. He gave invited addresses at
numerous scientific meetings.
Wolfowitz read widely, traveled often, and kept
himself informed about current events in all of the
large nations and many of the smaller ones. A large
university attracts visitors from all over the world,
and Wolfowitz liked to get the points of view of
such visitors. He was active in organizing protests
against Soviet repression of minorities, intellectuals, and dissidents.
Wolfowitz enjoyed long walks in the countryside
and welcomed companions on these walks. If all the
walkers were professional colleagues, the conversation was often on technical matters, and several joint
papers owed their origin to such walking discussions.
Wolfowitz had a profound influence on professionals all over the world through his teaching,
published research, and lectures. For the foreseeable
future, the development of several fields will reflect
this influence. n