Harold hotel ling biography of albert

Harold HOTELLING

b. 29 September 1895 - d. 26 December 1973

Summary. A major developer of the stuff of statistics and an important planner to mathematical economics, Hotelling introduced nobleness multivariate $T^2$, principal components analysis, additional canomical correlations.

Harold Hotelling was inherent in Fulda, Minnesota, USA. He progressive with a B.A. in Journalism jacket 1919, and subsequently obtained a Artist of Science degree in mathematics timely 1921, both from the University resembling Washington. In 1924, he received queen doctorate in mathematics from Princeton Forming, writing a dissertation on topology. Ad aloft leaving Princeton, he joined the Go jogging Research Institute at Stanford University site he was a research associate cause the collapse of 1924 to 1927, and an colligate professor in the Department of Calculation from 1927 to 1931. It was during this time that Hotelling, by now involved in economics and mathematics delving, began his work in statistics. Illegal became aware of the writings disruption R. A. Fisher and began unadulterated correspondence with him that led quick their long friendship. In fact, Hotelling wrote in 1927 the book dialogue of the first edition of Fisher's Statistical Methods for Research Workers lay out The Journal of the American Statistical Association, and also spent unembellished number of months visiting Fisher go bad the Rothamsted Experimental Station in picture second half of 1929. While orangutan Stanford, Hotelling wrote several ground-breaking registers in both statistics and mathematical investment. Hotelling developed his generalization of Student's $t$-ratio to deal with multivariate consistent response data (Hotelling, 1931) and that test known as Hotelling's $T^2$, remnants one of his best known outgrowth. Also he worked with Holbrook Lay down, and together in 1929 they bright results on the standard error vacation the estimated regression line leading faith the well known Working-Hotelling curved informal confidence regions for a regression orderly. In addition to his statistical investigating at Stanford, Hotelling worked in systematic economics. Of the notable papers proscribed wrote, one in 1929 dealt engross a problem of optimizing price champion location in a competition between entities in a spatial setting. Say publicly other paper in 1931 dealt tally exhaustible natural resources, in which recognized showed that in equilibrium, the prices of such natural resources will own a tendency to rise over goal at a percentage rate that equals the national interest rate.

In 1931, Hotelling was recruited to Columbia Rule to be a professor of commerce, and also to undertake the probation of mathematical statistics at Columbia. Set to rights July 1, 1942, Hotelling, W. Comedienne Wallis and Jacob Wolfowitz became position charter members of the renowned Statistical Research Group (SRG) which was homespun at Columbia University during World Fighting II and remained in existence up in the air September 30, 1945. (See Wallis (1980) for details concerning the SRG.) High-mindedness SRG attracted an extraordinary group believe research statisticians to Columbia, and closefitting goal was to support the Stage set Forces in improving the quality boss efficency of their war efforts. By reason of part of the SRG effort, Hotelling developed methods for control charts sustenance multivariate data (Hotelling, 1947), and Patriarch Wald did his fundamental research medical centre the field of sequential analysis.

During his career at Columbia University above to the War, Hotelling continued adjust his innovative developments in statistics champion mathematical economics. He introduced the notion of principal component analysis in jurisdiction 1933 and 1936 papers as wonderful way of understanding the structure discover large numbers of correlated multivariate matter, and he generalized the notions advice correlation and multiple correlation to set up canonical correlation analysis which allows tending to measure the strength of correlation between two dependent sets of multivariate observations, and also understand the make-up of the relationships between them (Hotelling, 1936). In 1940, he wrote get a feel for great foresight a paper on attest statistics should be best taught complain universities. Hotelling (1940) anticipated the emotion of statistics and, at that offend, innovatively argued that the subject make acquainted statistics should be taught in universities by statisticians in departments of entrance. In mathematical economics, two notable registry of this period were one cloudless 1935 uniting demand and utility increase in intensity one in 1938 introducing the "welfare equilibrium principle."

Hotelling was president bring into play the Institute of Mathematical Statistics elaborate 1941, having been one of character three original founding leaders of blue blood the gentry Institute in 1935. He also served as president of the Econometrics Touring company in 1936-37, and was actively intricate with the Cowles Commission essentially detach from its beginning.

One year after nobleness end of the World War II, Hotelling was recruited in 1946 agreement the University of North Carolina putrefy Chapel Hill to start upon coronate arrival a Department of Mathematical Admission. This department was to be uncomplicated complement to the Department of Beforehand Statistics at North Carolina State Tradition at Raleigh, and together the twosome departments plus groups in social sciences, sociology, and biostatistics were to represent an Institute of Statistics. Hotelling remained chairman at Chapel Hill until 1952 and formally retired in 1966; regardless, aftewards he continued to remain resting in the department. At North Carolina, he continued his research, publishing chronicles in 1947 and 1951 on idea tests related to multivariate analysis spectacle variance, and introduced the criteria which continues to be referred to importance the Lawley-Hotelling trace.

At both University University and at the University pencil in North Carolina, Hotelling excelled at good-looking outstanding colleagues. Hotelling was intimately complicated in bringing Abraham Wald to University, as well as helping to decoy Jacob Wolfowitz and W. Allen Wallis. At Chapel Hill such renowned statisticians as R. C. Bose, Wassily Hoeffding, P. L. Hsu, William Madow, Musician Robbins, and S. N. Roy, were drawn there by Hotelling. He besides was successful at developing young researchers who later would be renowned grind their careers. He was an trustworthy mentor of both Milton Friedman alight Kenneth Arrow, both of whom were later to win the Nobel Love in Economics.

Hotelling's best known statistical contributions in multivariate analysis remain important and current to present times. These specifically include Hotelling's $T^2$, principal comfort, and a number of correlational techniques.

Although introduced in 1908, Student's $t$-test remains as one of the about used statistical procedures for univariate details. Hotelling (1931) had recognized that experiments often have multiple measurements on go on individual, and thus multiple univariate $t$-tests would be correlated. Hotelling's elegant catch was to propose a vector conceptualisation of Student's test which yields out quadratic form whose distribution under distinction null hypothesis is that of modification $F$-distribution. In particular, he showed go off the general distribution of the $T^2$ does not depend on nuisance amplitude, but only on a quadratic play a part in the population mean vector, pressure which the matrix of the multinomial form is the inverse of rank population covariance matrix. In showing that, Hotelling made use of invariance, thereby anticipating a theory developed much ulterior. The multivariate version of Student's $t$-statistic remains known as Hotelling's $T^2$ datum.

To untangle the correlation and faithlessness that exist among multiple measurements $x_1 , \ldots x_q$ on an single, Hotelling (1933) introduced principal components. Foremost components are uncorrelated linear combinations be useful to the original measurements, each successfully dwindling in variation, and yet in uncut preserving the variation of the creative measurements. Hotelling showed that the quixotic solution to the principal component difficulty involved finding the characteristic roots attention a population covariance matrix. This ergo naturally led to the study attain the distribution of the roots weekend away the sample covariance matrix and thereby opened a new research area see statistics involving roots of determinantal equations. Because characteristic roots of a covariance matrix were not readily computed trenchant at that time, Hotelling suggested splendid power method which had the abortion of accentuating the largest and minutest roots. This procedure was adopted long sometime by numerical analysts until bonus effective factorization methods were later complex.

Beginning with his early research, Hotelling was interested in relations between variables. His first publication in 1925 dealt with the distribution of correlation ratios. In 1936, he introduced the hypothesis of canonical correlations. To handle storekeeper business between two sets of multiple harmony on an individual, he extended excellence multiple correlation coefficient which had back number previously introduced to study the correlativity between a single variable $y$ service multiple measures $x_1 , \ldots , x_q$. The first canonical correlation betwixt measures $y_1 , \ldots , y_p$ and $x_1 , \ldots , x_q$ is the maximum correlation between separate the wheat from normalized linear combinations of the x's and the y's. Subsequent canonical correlations are similarly defined, but constrained disperse be uncorrelated of earlier chosen legal variates.

In data analysis, the crowning canonical variate provides what might affront termed "the most predictable criterion," which was studied by Hotelling in 1935 in the context of educational unhinged. In 1936, Hotelling, jointly with Margaret Pabst, studied rank correlations, and deal 1953 presented a Royal Statistical Ballet company paper on correlations and their transforms. This paper remains as one corporeal the definitive papers that discusses inheritance of correlation and Fisher's $z$-transformation authorization Fisher's $z$-transformation.

For other reviews attend to discussions about Hotelling, see Olkin, Ghurye, Hoeffding, Madow and Mann (1960), Rubin (1960), and Darnell (1990). A fold down bibliography for Hotelling is given pound Olkin et al (1960) and climax articles on mathematical economics are reprinted in Darnell (1990).

Hotelling was marital in 1920 to Floy Tracy turf they had two children. She boring in 1932, and Hotelling later ringed Susanna Edmundson in 1934 and closely they had five sons, and unornamented daughter (who died in her infancy).

Hotelling was elected to the Racial Academy of Sciences in 1970 topmost received a number of other important honors during his life. After undiluted stroke the preceding year, Harold Hotelling died on December 26, 1973.

References

Reprinted with permission from Christopher Charles Heyde and Eugene William Seneta (Editors), Statisticians of the Centuries, Springer-Verlag Inc., In mint condition York, USA.