Some Analytical and Numerical Comparisons of Estimators for the Mixed A.O.V. Model
Ronald Raymond Hocking, Michael Kutner · Biometrics · 1975
The mixed A.O.V. model has been the subject of considerable discussion in the statistical literature. In particular, much attention has been given to the problem of point estimation: namely, the fixed effects and the variance components. Given estimates of the variance components, there is general agreement that the estimates of the fixed effects should be obtained from the Aitken equations (equation (3) below); hence most of the effort has been directed toward estimating the variance components. We have two objectives in writing this paper. The first is to present the likelihood equations in a form which not only allows for comparison with several other recently proposed estimators but also suggests an efficient computational procedure. The second obj ective is to provide numerical comparisons of these estimators. For the latter, we have selected the balanced incomplete block model (BIB) which has received some attention in the recent literature. (See e.g., Weeks and Graybill [1961], Low [1969], Basson [1970], and Rosenberg [1971].) The relative simplicity of this model also allows us to illustrate, in detail, the nature of the likelihood equations. We restrict our attention here to a small subset of the variance component literature. For an excellent review paper and an extensive bibliography, we refer to Searle [1971].