
Accession Number : AD0697399
Title : ON THE COSTWISE OPTIMALITY OF HIERARCHICAL MULTIRESPONSE RANDOMIZED BLOCK DESIGNS UNDER THE TRACE CRITERION,
Corporate Author : COLORADO STATE UNIV FORT COLLINS
Personal Author(s) : Srivastava,J. N. ; McDonald,L. L.
Report Date : SEP 1969
Pagination or Media Count : 20
Abstract : Consider the class of general incomplete multiresponse (GIM) designs in which the set of units is divided into blocks of equal size, such that in any block the same subset of responses is measured on each unit. It is shown that with respect to the trace criterion and a reasonable cost restriction, the subclass of hierarchical multiresponse (HM) designs is complete in the sense that given any GIM design, there exists a HM design such that the cost involved under the two designs is the same, but the trace of the covariance matrix of the estimates of the parameters under the HM design is less than or equal to the similar quantity under the GIM design. The results also establish the important fact that there is a large class of situations where the standard multiresponse model (under which all responses are measured on each unit) should not be used. The nonlinear programming problem associated with obtaining the optimum HM design is stated and solved. (Author)
Descriptors : (*COMBINATORIAL ANALYSIS, EXPERIMENTAL DESIGN), ANALYSIS OF VARIANCE, DECISION THEORY, NONLINEAR PROGRAMMING, OPTIMIZATION, THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE