Richard Loree Anderson

In 1942, Anderson found the probability density function of the serial correlation coefficient ${\displaystyle R_{N}:={\frac {X_{1}X_{L+1}+X_{2}X_{L+2}+\cdots +X_{N}X_{L}-(\sum _{i}X_{i})^{2}/N}{\sum _{i}X_{i}^{2}-(\sum _{i}X_{i})^{2}/N}}}$ when the variables ${\displaystyle X_{i}}$ are independent and identically distributed and follow the normal distribution.^[5] Anderson recalled that he preliminarily calculated this based on characteristic functions and presented it in the winter of 1940, but he thought it would be intractable for N > 9.^[4] The next day, he received a note from Cochran asking him to try out Cochran's theorem, which turned out to be the answer.^[4]

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.^[6]

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.^[7]

In 1985, Anderson, Sastry G. Pantula, and Larry A. Nelson, proposed an estimator for the covariance matrix for a mixed linear model, where the model describes an experiment conducted over several sites for several years.^[8] The model takes the form ${\displaystyle y_{ijk}=\sum _{m=1}^{s}x_{ijkm}\beta _{m}+u_{ijk}}$, where i indexes sites, j indexes "blocks" at each site, and k indexes treatments.^[8]

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.^[9]