Richard Loree Anderson (April 20, 1915 – February 19, 2003) was an American

econometrician Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics", '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8� ...

. He was a Professor of Statistics at

North Carolina State University North Carolina State University (NC State, North Carolina State, NC State University, or NCSU) is a public university, public Land-grant university, land-grant research university in Raleigh, North Carolina, United States. Founded in 1887 and p ...

from 1941 to 1966. In 1967, he took up chairmanship of the newly established Department of Statistics at the

University of Kentucky The University of Kentucky (UK, UKY, or U of K) is a Public University, public Land-grant University, land-grant research university in Lexington, Kentucky, United States. Founded in 1865 by John Bryan Bowman as the Agricultural and Mechanical ...

, a position he held until 1979. In 1951 he was elected as a

Fellow of the American Statistical Association Like many other academic professional societies, the American Statistical Association (ASA) uses the title of Fellow of the American Statistical Association as its highest honorary grade of membership. The designation of ASA Fellow has been a sign ...

. While a professor at the University of Kentucky, he consulted with a number of drug companies on clinical trials. Even before, he had been consulting several computer programming companies including IMSL, BMDP, and SAS. Anderson was good friends with

William Gemmell Cochran William Gemmell Cochran (15 July 1909 – 29 March 1980) was a prominent statistician. He was born in Scotland but spent most of his life in the United States. Cochran studied mathematics at the University of Glasgow and the University of Camb ...

before the latter died in 1980. The two had first met at

Iowa State University Iowa State University of Science and Technology (Iowa State University, Iowa State, or ISU) is a Public university, public land-grant university, land-grant research university in Ames, Iowa, United States. Founded in 1858 as the Iowa Agricult ...

in 1938.

Research

In 1942, Anderson found the

probability density function In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the s ...

of the serial correlation coefficient

R_N := \frac

when the variables

X_i

are

independent and identically distributed Independent or Independents may refer to: Arts, entertainment, and media Artist groups * Independents (artist group), a group of modernist painters based in Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist ...

and follow the

normal distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac ...

. Anderson recalled that he preliminarily calculated this based on

characteristic functions In mathematics, the term "characteristic function" can refer to any of several distinct concepts: * The indicator function of a subset, that is the function \mathbf_A\colon X \to \, which for a given subset ''A'' of ''X'', has value 1 at points o ...

and presented it in the winter of 1940, but he thought it would be intractable for ''N'' > 9. The next day, he received a note from Cochran asking him to try out

Cochran's theorem In statistics, Cochran's theorem, devised by William G. Cochran, is a theorem used to justify results relating to the probability distributions of statistics that are used in the analysis of variance. Examples Sample mean and sample variance ...

, which turned out to be the answer. In 1962, Anderson, W. T. Wells, and John W. Cell calculated the probability density function for the product of two noncentral chi-squared variables using the

Mellin transform In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral transform is closely connected to the theory of Dirichlet series, and is often used ...

. In 1980, Anderson, Walter W. Stroup, and James W. Evans devised an algorithm to compute maximum likelihood estimates for the completely random balanced incomplete block design. In 1985, Anderson, Sastry G. Pantula, and Larry A. Nelson, proposed an estimator for the

covariance matrix In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of ...

for a mixed linear model, where the model describes an experiment conducted over several sites for several years. The model takes the form

y_ = \sum_^s x_\beta_m + u_

, where ''i'' indexes sites, ''j'' indexes "blocks" at each site, and ''k'' indexes treatments. In 1996, Anderson, Pao-Sheng Shen, and P. L. Cornelius used simulations to study nested mating designs. They concluded that asymptotic variances severely underestimate the actual variance in the simulation.

References

External links

Material at NCSU Library
1915 births 2003 deaths People from St. Joseph County, Indiana American statisticians DePauw University alumni Iowa State University alumni North Carolina State University faculty University of Kentucky faculty Fellows of the American Statistical Association {{US-statistician-stub