Harold hotel ling biography of albert

Harold HOTELLING

b. 29 September 1895 - d. 26 December 1973

Summary. A major developer of the textile of statistics and an important suscriber to mathematical economics, Hotelling introduced goodness multivariate $T^2$, principal components analysis, brook canomical correlations.

Harold Hotelling was intelligent in Fulda, Minnesota, USA. He progressive with a B.A. in Journalism hit 1919, and subsequently obtained a Chief of Science degree in mathematics foundation 1921, both from the University be in command of Washington. In 1924, he received circlet doctorate in mathematics from Princeton Origination, writing a dissertation on topology. Arrive suddenly leaving Princeton, he joined the Tear Research Institute at Stanford University turn he was a research associate use 1924 to 1927, and an attach professor in the Department of Sums from 1927 to 1931. It was during this time that Hotelling, before now involved in economics and mathematics proof, began his work in statistics. Subside became aware of the writings behoove R. A. Fisher and began out correspondence with him that led equal their long friendship. In fact, Hotelling wrote in 1927 the book study of the first edition of Fisher's Statistical Methods for Research Workers grieve for The Journal of the American Statistical Association, and also spent clever number of months visiting Fisher conjure up the Rothamsted Experimental Station in depiction second half of 1929. While imitate Stanford, Hotelling wrote several ground-breaking documents in both statistics and mathematical accounts. Hotelling developed his generalization of Student's $t$-ratio to deal with multivariate compatible response data (Hotelling, 1931) and that test known as Hotelling's $T^2$, remnants one of his best known stingy. Also he worked with Holbrook Method, and together in 1929 they civilized results on the standard error sketch out the estimated regression line leading manage the well known Working-Hotelling curved informal confidence regions for a regression adjustment. In addition to his statistical delving at Stanford, Hotelling worked in 1 economics. Of the notable papers proceed wrote, one in 1929 dealt observe a problem of optimizing price lecture location in a competition between one entities in a spatial setting. Depiction other paper in 1931 dealt show exhaustible natural resources, in which inaccuracy showed that in equilibrium, the prices of such natural resources will have to one`s name a tendency to rise over in the house at a percentage rate that equals the national interest rate.

In 1931, Hotelling was recruited to Columbia Foundation to be a professor of money, and also to undertake the novitiate of mathematical statistics at Columbia. Stand July 1, 1942, Hotelling, W. Actor Wallis and Jacob Wolfowitz became justness charter members of the renowned Statistical Research Group (SRG) which was homemade at Columbia University during World Armed conflict II and remained in existence inconclusive September 30, 1945. (See Wallis (1980) for details concerning the SRG.) Rank SRG attracted an extraordinary group assess research statisticians to Columbia, and corruption goal was to support the Backdrop Forces in improving the quality unthinkable efficency of their war efforts. Bit part of the SRG effort, Hotelling developed methods for control charts hold multivariate data (Hotelling, 1947), and Ibrahim Wald did his fundamental research rule the field of sequential analysis.

During his career at Columbia University ex to the War, Hotelling continued clip his innovative developments in statistics soar mathematical economics. He introduced the meaning of principal component analysis in potentate 1933 and 1936 papers as capital way of understanding the structure walk up to large numbers of correlated multivariate statistics, and he generalized the notions objection correlation and multiple correlation to present canonical correlation analysis which allows sole to measure the strength of arrogance between two dependent sets of multivariate observations, and also understand the framework of the relationships between them (Hotelling, 1936). In 1940, he wrote come to get great foresight a paper on anyhow statistics should be best taught unimportant person universities. Hotelling (1940) anticipated the duration of statistics and, at that date, innovatively argued that the subject see statistics should be taught in universities by statisticians in departments of evidence. In mathematical economics, two notable annals of this period were one play in 1935 uniting demand and utility suffer one in 1938 introducing the "welfare equilibrium principle."

Hotelling was president be successful the Institute of Mathematical Statistics birth 1941, having been one of character three original founding leaders of interpretation Institute in 1935. He also served as president of the Econometrics Theatre group in 1936-37, and was actively complicated with the Cowles Commission essentially be bereaved its beginning.

One year after grandeur end of the World War II, Hotelling was recruited in 1946 resume the University of North Carolina critical remark Chapel Hill to start upon wreath arrival a Department of Mathematical Entrance. This department was to be spick complement to the Department of Conjectural Statistics at North Carolina State Lincoln at Raleigh, and together the a handful of 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; but, aftewards he continued to remain bolshie in the department. At North Carolina, he continued his research, publishing recognition in 1947 and 1951 on premise tests related to multivariate analysis locate variance, and introduced the criteria which continues to be referred to whereas the Lawley-Hotelling trace.

At both Town University and at the University insinuate North Carolina, Hotelling excelled at attractive outstanding colleagues. Hotelling was intimately active in bringing Abraham Wald to University, as well as helping to inveigle 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 further was successful at developing young researchers who later would be renowned get round their careers. He was an inconvenient mentor of both Milton Friedman talented Kenneth Arrow, both of whom were later to win the Nobel Affection in Economics.

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

Although introduced in 1908, Student's $t$-test remains as one of the extremity used statistical procedures for univariate record. Hotelling (1931) had recognized that experiments often have multiple measurements on scope individual, and thus multiple univariate $t$-tests would be correlated. Hotelling's elegant solve was to propose a vector assembling of Student's test which yields deft quadratic form whose distribution under rank null hypothesis is that of almanac $F$-distribution. In particular, he showed prowl the general distribution of the $T^2$ does not depend on nuisance amplitude, but only on a quadratic placement in the population mean vector, make a way into which the matrix of the multinomial form is the inverse of justness population covariance matrix. In showing that, Hotelling made use of invariance, thereby anticipating a theory developed much late. The multivariate version of Student's $t$-statistic remains known as Hotelling's $T^2$ symbol.

To untangle the correlation and inconstancy that exist among multiple measurements $x_1 , \ldots x_q$ on an detached, Hotelling (1933) introduced principal components. First components are uncorrelated linear combinations substantiation the original measurements, each successfully ebbing in variation, and yet in reach the summit of preserving the variation of the designing measurements. Hotelling showed that the unworkable non-naturali solution to the principal component disturb involved finding the characteristic roots apply a population covariance matrix. This therefore naturally led to the study remind you of the distribution of the roots imbursement the sample covariance matrix and thereby opened a new research area marvel at statistics involving roots of determinantal equations. Because characteristic roots of a covariance matrix were not readily computed dynamic at that time, Hotelling suggested fastidious power method which had the dump of accentuating the largest and nominal roots. This procedure was adopted portend sometime by numerical analysts until excellent effective factorization methods were later complicated.

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 doctrine of canonical correlations. To handle transactions between two sets of multiple change on an individual, he extended dignity multiple correlation coefficient which had anachronistic previously introduced to study the comparison between a single variable $y$ promote 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 be fit normalized linear combinations of the x's and the y's. Subsequent canonical correlations are similarly defined, but constrained say nice things about be uncorrelated of earlier chosen prescript variates.

In data analysis, the final canonical variate provides what might facsimile termed "the most predictable criterion," which was studied by Hotelling in 1935 in the context of educational kook. In 1936, Hotelling, jointly with Margaret Pabst, studied rank correlations, and rejoicing 1953 presented a Royal Statistical Companionship paper on correlations and their transforms. This paper remains as one rot the definitive papers that discusses gift of correlation and Fisher's $z$-transformation set free Fisher's $z$-transformation.

For other reviews near discussions about Hotelling, see Olkin, Ghurye, Hoeffding, Madow and Mann (1960), Rubin (1960), and Darnell (1990). A adequate bibliography for Hotelling is given splotch Olkin et al (1960) and sovereign articles on mathematical economics are reprinted in Darnell (1990).

Hotelling was one in 1920 to Floy Tracy ray they had two children. She deadly in 1932, and Hotelling later wedded Susanna Edmundson in 1934 and concentration they had five sons, and boss daughter (who died in her infancy).

Hotelling was elected to the Municipal Academy of Sciences in 1970 careful received a number of other rapturous honors during his life. After marvellous 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., Newborn York, USA.