Optimal design of complex experiments with qualitative factors of influence

A complex experiment with qualirarive factors influencing the outcome of the experiment can be seen as a general ANOVA setup. A design of such an experiment will be the assignment at which of the possible levels of the factors the actual experiment should be performed. In this paper optimal designs of such experiments will be characterized with respect to three different optimality criteria including the so called uniform optimality of a design. The possible applications of the main optimization result providing these characterizations can be used to more general experiments. The particular results on these generalizations will be indicated at the end of this paper.     

Progressively censored tests for clinical experiments and life testing problems based on weighted empirical distributions

In the context of time-sequential studies, progressively censored tests for a simple regression model based on weighted empirical distributions are considered for ungrouped as well as grouped data situations. Early decision rules based on such tests are formulated. The asymptotic theory of the proposed tests rests on a construction of suitable empirical processes and their convergence (in distribution) to appropriate Gaussian functions. Critical values of the proposed test statistics are obtained by simulation, For a hypothetical example (of practical interest), a comparative study is made for the empirical powers and stopping times for some rival tests.     

Use of the 21% rulf in experimental design

When the probabilities underlying a contingency table are assumed to be symmetric, it is advantageous to combine the frequencies of equiprobable cells (Haber, 1981, 1982).The present work introduces models, as well as exact and asymptotic methods, for analyzing such ‘intraclass’ contingency tables in several dimensions.     

Constructions of efficiency-balanced designs

We present a number of methods of constructing efficiency-balanced binary block designs which are design patterns for simplification of statistical analysis. Furthermore, a method of construction of an efficiency-balanced block design with v+1 treatments from one with v treatments is generally characterized.     

On the recovery of intra- and interblock information in n-ary designs

This note presents an extension of Q-method of analysis for binary designs given by Rao (1956) to n-ary balanced and partially balanced block designs. Here a linked n-ary block (LNB) design is defined as the dual of balanced n-ary (BN) design. Having a note on Yates’ (1939, 1940) method of P-analysis, we further extend the expressions for binary linked block (LB) designs given by Rao (1956) to linked n-ary block (LNB) designs which admit easy estimation of parameters for these type of all n-ary designs.     

The mad estimator: when is it non-linear? applications to two-way design models

The mean absolute deviation (MAD) estimator has recently received a great deal of attention as applied to full-rank linear regression models. This paper provides a necessary and sufficient condition for the MAD estimator to be a non-linear estimator, in which case conditions for the variance of the MAD estimator to be larger or smaller than those for OLS are, in general, unknown. The non-linearity of the MAD estimator is examined for several two-way designs; in particular (1) randomized block design (2) two-way nested design (3) two-way classification with interaction and (4) partially balanced incomplete block design     

Use of balanced bipartite weighing designs as chemical balance designs

This paper deals with the use of balanced bipartite weighing designs as chemical balance designs when there Is a restriction on the number of objects that can be placed on either pan..The variance of each estimated weight and the covarlance of each pair of estimated weights are worked out.The use of additional weighing when the design matrix is singular is discussed.     

Statistical methodology for binary data from a set of partially structured two-way random cross-classifications

A complete two-way cross-classification design is not practical in many settings. For example, in a toxicological study where 30 male rats are mated with 30 female rats and each mating outcome (successful or unsuccessful)is observed, time and resource considerations can make the use of the complete design prohibitively costly. Partially structured variations of this design are, therefore, of interest (e.g., the balanced disjoint rectangle design, the fully diagonal design, and the "S"-design). Methodology for analyzing binary data from such incomplete designs is illustrated with an example. This methodology, which is based on infinite population sampling arguments, allows the estimation of the mean response, among-row correlation coefficient, among-column correlation coefficient, and the within-cell correlation coefficient as well as their standard errors.