Harold Hotelling

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Harold Hotelling (Fulda, Minnesota, September 29, 1895 - December 26, 1973) was a mathematical statistician, and very influential economic theorist. His name is known to all statisticians because of Hotelling's T-square distribution and its use in statistical hypothesis testing and confidence regions. He also introduced canonical correlation analysis, and is the eponym of Hotelling's law, Hotelling's lemma, and Hotelling's rule in economics.

He was a member of the faculty of Columbia University from 1931 until 1946, and a member of the department of statistics at the University of North Carolina at Chapel Hill from 1946 until his death. A street in Chapel Hill bears his name. In 1972 he received the North Carolina Award for contributions to science.

The historian Stephen Stigler has said that it was because of Hotelling's suggestion in a letter to R.A. Fisher that cumulants are known by their now-standard name.

His economics papers have inspired research agenda in several areas still active. Hotelling has a crucial place in the pedigree of modern economic theory. While at the University of Washington, he was encouraged to switch from pure mathematics toward mathematical economics by the famous mathematician Eric Temple Bell. Later at Columbia University in the 40s, Hotelling in turn encouraged young Kenneth Arrow to switch from mathematics and statistics applied to acturial studies towards more general applications of mathematics in general economic theory. This line of development of economic thought stretches all the way from Adam Smith to present-day cutting edges of economic theory, with Kenneth Arrow, now in active retirement, still participating. In the early 1950s, Arrow co-authored with Gerard Debreu a mathematical rigorous proof of the existence of a general equilibrium for a market economy, just what Adam Smith had predicted in eloquent literary terms with his Invisible Hand theorem in "The Wealth of Nations" back in 1776. Smith, Hotelling, Arrow and Debreu all cast long shadows.

[edit] Works

"A General Mathematical Theory of Depreciation", 1925, Journal of ASA.
"Differential Equations Subject to Error", 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", Proc. Second Berkley Symposium of Mathematical Statistics and Probability, 1951