Comparisons of Designs and Estimation Procedures for Estimating Parameters in a Two-Stage Nested Process

C. R. Henderson, the Statistician; And His Contributions to Variance Components Estimation

“…The few numerical studies that were done (e.g. Bainbridge, 1963, Bush and Anderson, 1963, Anderson and Crump, 1967, and Anderson, 1975 are mostly for small hypothetical data layouts that give little or no relevant information for the kind of large data sets that animal breeders so often deal with.…”

Variance components — some history and a summary account of estimation methods

“…In that paper the ANOVA method of estimation, based on equating analysis of variance sums of squares to their expected values, was extended for unbalanced data to equating a wide variety of quadratic forms (not all of them sums of squares) to their expected values. Then followed a period of trying to evaluate those methods mostly through deriving expressions, under normality assumptions, for sampling variances of the resulting estimates, e.g., Crump (1951), Searle (1956Searle ( , 1958Searle ( , 1961, Mahamunulu (1963), Low (1964), Hirotsu (1966), Blischke (1966Blischke ( , 1968, and Rohde and Tallis (1969 Anderson, 1975, Anderson and Crump, 1967, Bainbridge, 1963 gives some indication of which of some applications of the ANOVA methods may be better than others for quite a variety of special designs planned for estimating variance components. But it can be difficult to extrapolate from those designs to situations often found with survey-style data; for example, to breeding data from farm livestock, where there may be several hundreds of levels of a random factor, and some thousands of cells in the data but with only 20-30% of them actually containing data.…”

D-Optimal Split-plot Designs With Random Whole Plot Factor and Fixed Sub-plot Factor

“…The solution also depends on the model and the method of estimation one-way random model. Crump's result was later published by Anderson and Crump (1967). They showed that for a fixed number of experimental runs and a fixed number of levels of the random factor, the 𝑉𝑎𝑟(𝜎 𝛼 2 ) and𝑉𝑎𝑟 (𝜎 𝛼 2 𝜎 𝑒 2 ⁄ ) are minimized when there is an almost equal allocation of observation into each level of the random factor.…”