Abstract
This dissertation deals with the practical solution of estimation and classification problems which arise in the fixed model analysis of variance when one encounters responses which are not completely specified, and may, therefore, be said to be "unclassified" responses. Rather than discard these unclassified responses, a new approach is being developed in which all available information from a study (survey or experiment) is employed in the estimation of the parameters. This somewhat unusual problem has been described and a general solution developed for it by H. 0. Hartley and J. N. K. Rao. In particular, this study develops a feasible solution for the problem mentioned above when the number (k) of "cells" from which each unclassified response (y (i with a star above)) may have arisen and the number (m) of these responses are both moderately large. In such situations the computational effort is involved in locating the single "placement" ( i. e ., the feasible global minimum, u(s)) of the k (to the power of m) possible placements (and corresponding values u (i)) for which a "decision function" based on minimal residual "sum of squares", is an absolute minimum may well be prohibitive, even with electronic data processing equipment. The solution developed here relies upon either an iterative scheme which converges to a (possibly local) feasible minimum or a search technique (also called a check procedure) which "searches" a certain number of m-dimensional cubes enclosing the non-feasible global minimum, or both. The iterative procedure is a two-stage cyclic operation in which the magnitude of the quadratic form must decrease at each stage. The search procedure is based upon an inequality which requires knowledge of the upper bound of the maximum eigenvalue of a certain class of positive definite matrices..
Johnston, Walter Edward (1971). Estimation and classification problems in the fixed model analysis of variance. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -178448.