
Harold Hotelling
18951973

by Megan Kruse Public Affairs Coordinator, ASA
Harold Hotelling was born in Minnesota in 1895 and spent most of his
childhood in Seattle, Washington. He earned a bachelor's degree in journalism
in 1919 and a master's degree in mathematics in 1921 from the University
of Washington. In 1924, he earned a PhD in mathematics from Princeton
University, and began teaching at Stanford University that same year.
Hotelling soon realized that the field of statistics would be more useful if
it employed methods of higher mathematics, so in 1929, he went to England to
study with R. A. Fisher, a very prominent statistician. When Hotelling returned
to the United States, he began developing some of his techniques at Stanford
University. His early applications involved the diverse fields of journalism,
political science, population, and food supply.
In 1931, Hotelling began working at Columbia University, where he was
instrumental in the creation of the university's statistics department.
During his time at Columbia, he helped several Central European scholars,
including the late Abraham Wald, escape Germany, and conducted militaryrelated
statistical work during World War II.
"Qualifications of a good teacher of statistics include, first
and foremost, a thorough knowledge of the subject. This statement seems
trivial, but it has been ignored in such a way as to bring about the present
unfortunate situation. Mathematicians and others, who deplore the tendency
of Schools of Education to turn loose on the world teachers who have not
specialized in the subject they are to teach, would do well to consider
their own tendency to entrust the teaching of statistics to persons who
not only have not specialized in the subject, but have no sound knowledge
of it whatever," Hotelling said around 1940.
Gertrude Cox, the first director of the Institute of Statistics, recruited
Hotelling for the University of North Carolina at Chapel Hill (UNCCH)
in 1946 to found a new statistics department. At the University, he was
a professor and chair of the Department of Mathematical Statistics, a
professor of economics, and associate director of the Institute of Statistics.
In 1961, he was promoted to Kenan Professor of Statistics. He retired
from the university in 1966. In 1989, the UNCCH established the Harold
Hotelling Professorship in Economics to honor Hotelling and his works.
Hotelling was considered a pioneer in the field of mathematical statistics
and economics in the 20th century, with contributions to the theory of
demand and utility, welfare economics, and taxation. His work in mathematical
statistics included his famous 1931 paper on the Student's t distribution
for hypothesis testing, in which he laid out what has since been called
"confidence intervals." His economics papers throughout the
1920s and 1930s discussed competition, gametheory, depreciation, and
resource exhaustion. He also covered topics in mathematical statistics
such as hypothesis testing and confidence intervals.
The area of statistics with the most sustained and probably most significant
efforts of Hotelling is multivariate statistical analysis. In fact, his
name is associated with several methods and statistics. His first significant
contribution came to be called Hotelling's Generalized T2. Another major
development in multivariate analysis linked to Hotelling is principal
components. He precisely formulated the idea of component, bringing to
bear the mathematical knowledge, pointing out the implications, setting
forth computational procedures, and discussing statistical inference.
When Hotelling and his wife first arrived in Chapel Hill, they also instituted
the "Hotelling Tea," where they opened their home to students
and faculty for tea time once a month.
In 1953, Hotelling published a paper of over 30 pages on the distribution
of the correlation coefficient. (See the previous article on F. N. David
in this issue of Amstat News.) F. N. David, who did a tremendous amount
of hard computing to publish the tables in 1938, understandably "felt
rather peevish" when she read his paper and found that he had put
the distribution in various forms, of which some lead to more efficient
calculating methods than were previously available.
After R.A. Fisher's 1922 paper on maximum likelihood estimates, a stream of
papers followed on the consistency and asymptotic normality of such estimates.
Among the first of these was Hotelling's in 1930. It was an attempt to state
precise conditions for consistency and asymptotic normality and give rigorous
proofs of the theorems. This work came closer to providing satisfactory mathematical
treatment, though it was not altogether successful.
Hotelling's publications include research in mathematics, mathematical economics,
and theoretical and applied statistics, educational philosophies and discussions,
biographical sketches, book reviews, and other assorted papers. Early papers
explored statistical topics such as the density of the correlation coefficient,
differential equations having probability error terms, and stochastic processes.
Over the years, he covered many other statistical problems and pioneered many
new developments.
Hotelling ensured that his economics students were wellversed in statistical
theory, and he helped teach many future economists and statisticians.
In a tribute to Hotelling, William Madow said of Hotelling's students,
"Above all, they come to want to be statisticians, to do research,
to teach, to apply and to consult, and to feel they can do it." In
1940, Hotelling wrote a paper about the future of statistical education
in which he asked whether statistics should be taught in departments such
as business, engineering, psychology, or sociology, or given its own department
within colleges and universities. Over 60 years later, significant progress
has been made in recognizing the importance of statistical education in
all fields of study, due in part to Hotelling's writings on education.
In addition to his teaching, writing, and professional activities, Hotelling
served on the editorial boards of the Annals of Mathematical Statistics
and the American Journal of Economics and Sociology. He was elected president
of the Institute of Mathematical Statistics and the Econometric Society.
He was also elected Fellow of the American Statistical Association in
1937 and served as its vice president in 1941.
Hotelling died in 1973 after a successful career at several prominent universities
and the creation of two strong statistics programs.