# Accession Number:

## AD0697399

# Title:

## ON THE COSTWISE OPTIMALITY OF HIERARCHICAL MULTIRESPONSE RANDOMIZED BLOCK DESIGNS UNDER THE TRACE CRITERION,

# Descriptive Note:

# Corporate Author:

## COLORADO STATE UNIV FORT COLLINS

# Personal Author(s):

# Report Date:

## 1969-09-01

# Pagination or Media Count:

## 20.0

# 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:

# Subject Categories:

- Statistics and Probability