Herman Chernoff is
emeritus professor of statistics at Harvard
University and emeritus professor of applied
mathematics at the Massachusetts Institute of
Technology (MIT). Throughout his career,
Herman made many long-lasting contributions as
a scholar and teacher in statistical science,
with many contributions bearing his name, from
foundational measures such as “Chernoff
distribution” to mathematical theorems such as
the “Chernoff bound” to practical tools such
as “Chernoff faces.” As a preeminent scholar
in Statistics, he has received numerous
honors, including being elected as the
president of the Institute of Mathematical
Statistics and as an elected member of both
the American Academy of Arts and Sciences and
the National Academy of
Sciences. A symposium
in honor of Herman in celebration of his 95th
birthday was held at Harvard University on
April 27, 2018, and NESS Council is in the
process of establishing the Herman Chernoff
Award in his honor.
Herman was born in New York City on July 1,
1923. He attended junior high school in New
York and, because he had shown considerable
ability, was invited to take the competitive
examinations to enter Townsend Harris High
School. This was a particularly prestigious
school that acted as a preparatory school for
those who went on to attend the City College
of New York. After successfully attending
Townsend Harris High School, he entered the
City College of New York. There he earned his
B.S. degree from the City College of New York
in 1943, majoring in mathematics with a minor
in physics. He received his Ph.D. degree in
1948 from Brown University under the guidance
of Abraham Wald at Columbia University.
His first published paper in statistics, and
part of his thesis, is titled “Asymptotic
Studentization in Testing of Hypotheses.”
From 1947 to 1949, Herman worked as a
research associate at the Cowles Commission
for Research in Economics at the University
of Chicago, where several associates would
eventually earn Nobel Memorial Prizes in
Economic Sciences for research performed at
the Cowles Commission. He worked with Herman
Rubin (currently an eminent professor of
statistics and mathematics at Purdue
University) and Kenneth Arrow (who was
awarded the Nobel Prize in Economics in
1972) during his time at the Cowles
Commission. From 1949 to 1952, Herman was on
the faculty of the Department of Mathematics
at the University of Illinois at Urbana,
where he was appointed to associate
professor in 1950. While taking leave from
there, he was invited by Kenneth Arrow to
visit Stanford University from the summer of
1951 to January 1952. While at Stanford, he
accepted a permanent position in the
Department of Statistics at Stanford
University in 1952 and started as an
associate professor before becoming
professor in 1956. He remained at Stanford
University for 22 years. During his early
years at Stanford University, he worked on
the topics “Measure of Asymptotic
Efficiency,” which led to the result later
known as “Chernoff’s bound,” and “Locally
Optimal Designs.”
Regarding the later, if there is interest
in estimating a parameter when there are
several nuisance parameters, Herman was able
to show that, if there are k parameters
altogether and interest is in one function of
these parameters, then a researcher needs at
most k of the experiments that are available
to be performed, in certain proportions, to
get an (asymptotically) optimal design;
therefore, for a problem where experiments
yield data depending on k parameters and only
one is to be estimated, an optimal design
requires at most k of the available
experiments to be repeated independently in
certain proportions. This result generalizes
so that if a researcher wants to estimate two
functions of the parameters, then he or she
would need at most [k + (k-1)] of the
available experiments.
Following his early works, Herman
contributed significantly in sequential
testing of hypotheses where there is an
incentive to use a mixture of experiments. He
proved the asymptotic optimality of a
sequential design procedure using randomized
experiments, Kullback-Leibler information
numbers, and a trivial stopping rule, assuming
that there were only a finite number of states
of nature and a finite number of distinct
experiments available. This result was later
generalized by his students and other
researchers.
His contribution to nonparametric
statistics was collaborative with Richard
Savage when they worked on Lehmann and Hodges
conjecture regarding a nonparametric
competitor to the t-test. This scholarship
gave rise to the result known as the
“Chernoff-Savage theorem.” In the 1970s,
Herman also worked on multivariate analysis
where he creatively used human faces, known
widely now as “Chernoff faces,” to visualize
high-dimensional data. In general, Herman has
worked on many highly theoretical topics and
real-life applications, including an
examination
of an FBI report that claimed to prove that
President Kennedy was killed by a shot from
the Grassy Knoll at Dealey Plaza.
In 1974, Herman moved to the MIT as a
professor of applied mathematics with the
expectation to develop a statistics program
with a strong emphasis on applications. During
his years at the MIT, he wrote about the
Massachusetts Number Game and became also
interested in statistical problems in the
lottery. In 1984 he joined the Department of
Statistics at Harvard University, where he
retired in 1997, but remains on ongoing
presence in the department and continues with
research activities.
