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 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.
In fact Hotelling could trace his family back much further than the seventeenth century, to important people in England and Holland.
The area of statistics with the most sustained and probably most significant efforts of Hotelling is multivariate statistical analysis. Hotelling is known to statisticians because of Hotelling's T-square distribution and its use in statistical hypothesis testing and confidence regions. He also introduced canonical correlation analysis.
The Methodist Church in Seattle became a major focus for the family.
The young Hotelling was an avid reader, making great use of the Seattle Public Library. During his years at high school he studied mathematics, science and classics but he was particularly interested in electricity reading every book he could find on the topic.
He worked for several small newspapers while he was undertaking his undergraduate studies, and he also made use of his knowledge of electricity by doing wiring jobs. He majored in journalism, but took a couple of mathematics courses taught by Eric Temple Bell who spotted his talent. However, before completing the course, he was called up for war service during World War I. Despite his obvious academic talents, the army decided that he was best suited to looking after mules. This turned out to be a blessing in disguise for one of the temperamental mules (called Dynamite) kicked him and broke his leg. Although this does not look like a blessing, we note that he did not see active service because of this while the other members of his division were sent to France where the majority were killed. He was discharged from the army on 4 February 1919 and resumed his studies at Washington University. He graduated with a B.A. in 1919 and took a job as a journalist with the Washington Standard. However, he did not find the work attractive and, persuaded by E T Bell, he returned Washington University in January 1920 to study for a Master's degree in mathematics.
The year 1931 was significant for Hotelling in another way for, in that year, he left Stanford University to take up a professorship in the Economics Department of Columbia University.
Following the award of his doctorate, Hotelling was appointed as a junior associate at the Food Research Institute attached to Stanford University. In 1925 his thesis was published as well as two important papers "A general mathematical theory of depreciation on mathematical economics, and The distribution of correlation ratios calculated from random data".
The year 1931 was significant for Hotelling in another way for, in that year, he left Stanford University to take up a professorship in the Economics Department of Columbia University. There he taught courses on economics but most of his energy for research was put into developing statistics.
Hotelling left Columbiain 1946 to start up a Department of Mathematical Statistics at the University of North Carolina at Chapel Hill. He was chairman of the Department as well as associate director of the Institute of Statistics.
He was elected a fellow of the American Statistical Association in 1937, serving as its vice president in 1941. He also served as president of the Institute of Mathematical Statistics.
"A General Mathematical Theory of Depreciation", 1925, Journal of ASA.
"Differential Equations Subject to Error", 1927, Journal of ASA
Review of R. A. Fisher's Statistical Methods for Rearch Workers,1927. Journal of ASA
"Applications of the Theory of Error to the Interpretation of Trends", with H. Working, 1929, Journal of ASA.
"Stability in Competition", 1929, EJ.
"The Economics of Exhaustible Resources", 1931, JPE.
"The Generalization of Student's Ratio", 1931, Annals of Mathematical Statistics.
"Edgeworth's Taxation Paradox and the Nature of Supply and Demand Functions", 1932, JPE.
"Analysis of a Complex of Statistical Variables with Principal Components",1933, Journal of Educational Psychology
"Demand Functions with Limited Budgets", 1935, Econometrica.
"The most predictable criterion", 1935, Journal of Educational Psychology
"Relation Between Two Sets of Variates", 1936, Biometrika.
"Rank Correlation and Tests of Significance Involving no Assumption of Normality", in "American Mathematical Statistics", 1936 (coauthor M. R. Pabst)
"The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates", 1938, Econometrica.
"A generalized T-Test and measure of multivariate dispersion", Proceedings Second Berkeley Symposium of Mathematical Statistics and Probability, 1951
Hotelling, Harold (1988). "Golden Oldies: Classic Articles from the World of Statistics and Probability: 'The Place of Statistics in the University'"
Hotelling, Harold (1988). "Golden Oldies: Classic Articles from the World of Statistics and Probability: 'The Teaching of Statistics'"
In his life Hotelling would not be religious, nevertheless he retained the strong beliefs in social justice, and the abhorrence of alcohol and tobacco, which came from the Church.
In his 1929 paper entitled “Stability in Competition,” Harold Hotelling suggested that political candidates’ platforms seem to converge during majoritarian elections. Hotelling compared political elections to businesses in the private sector. He postulated that just as there is not a striking difference between salesmen's products, so, too, there is not a stark contrast between politicians' platforms. This is because politicians, just like salesmen with consumers, seek to capture the majority of voters. Duncan Black, in his 1948 paper titled “On the Rationale of Group Decision-making,” a work on majority voting, made the theorem and its assumptions explicit. Black wrote that he saw a large gap in economic theory concerning how voting determines the outcome of decisions, including political decisions. Black’s paper thus began the long line of research that was to follow on how economics can explain voting systems.
"He, who doesn't conduct research, cannot teach others".