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Harold Hotelling 

Harold  Hotelling

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 military-related 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 (UNC-CH) 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 UNC-CH 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, game-theory, 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 well-versed 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.