A note on the connectivity of generalized cyclic designs

A necessary and sufficient condition is given to ensure that a generating blook of a generalized cyclic design will give rise to a connected design. The use of disconnected designs is briefly discussed.     

Improved estimation of variance components in mixed models

Taking Albert's (1976) formulation of a mixed model ANOVA, we consider improved estimation of the variance components for balanced designs under squared error loss. Two approaches are presented. One extends the ideas of Stein (1964), The other is developed from the fact that variance components can be expressed as linear combinations of chi-square scale parameters. Encouraging simulation results are presented.     

A bayesian approach to the comparison of two means

A hierarchical Bayesian approach to the problem of comparison of two means is considered. Hypothesis testing, ranking and selection, and estimation (after selection) are treated. Under the hypothesis that two means are different, it is desired to select the population which has the larger mean. Expressions for the ranking probability of each mean being the larger and the corresponding estimate of each mean are given. For certain priors, it is possible to express the quantities of interest in closed form. A simulation study has been done to compare mean square errors of a hierarchical Bayesian estimator and some of the existing estimators of the selected mean. The case of comparing two means in the presence of block effects has also been considered and an example is presented to illustrate the methodology.     

A class of new pbib designs

Two series of PBIB designs, one with three associate classes and theother with four associate classes ars developed. Efficiency factors for two designs are computed.     

Adaptive choice of scale tests in flexible two-stage designs with applications in experimental ecology and clinical trials

In this paper, the two-sample scale problem is addressed within the rank framework which does not require to specify the underlying continuous distribution. However, since the power of a rank test depends on the underlying distribution, it would be very useful for the researcher to have some information on it in order to use the possibly most suitable test. A two-stage adaptive design is used with adaptive tests where the data from the first stage are used to compute a selector statistic to select the test statistic for stage 2. More precisely, an adaptive scale test due to Hall and Padmanabhan and its components are considered in one-stage and several adaptive and non-adaptive two-stage procedures. A simulation study shows that the two-stage test with the adaptive choice in the second stage and with Liptak combination, when it is not more powerful than the corresponding one-stage test, shows, however, a quite similar power behavior. The test procedures are illustrated using two ecological applications and a clinical trial.     

An algorithn for generating a basis of the trades on t-designs

For the purpose of constructing t-designs (a special family of incomplete block designs) from a given design, a trade off method has been introduced and studied [Hedayat and Li (1979)]. In this paper, we present a computer algorithm for generating a basis of the trades on t-designs utilizing the results of Graham, Li and Li (1980).     

Monotony relations between distribution functions and their application to experimental design

In a linear regression model an estimator of the unknown coefficients is considered which, in special cases, includes the least squares estimator. In the ease of stable symmetric error distribution and by means of a certain monotony relation between distribution functions optimality of this estimator is proved and the designing problem is investigated. A robustness property of optimal designs against the designing criterion and some conclusions are given concerning the least squares estimator in the case of G- and C-optimality.     

Calibrated Estimators of Population Mean for a Mail Survey Design

In this article, we consider the problem of estimating the population mean of a study variable in the presence of non-response in a mail survey design. We introduce calibrated estimators of the population mean of a study variable in the presence of a known auxiliary variable. Using simulation the proposed calibrated estimators of population mean are compared to the Hansen and Hurwitz (1946) estimator under different situations for fixed cost as well for fixed sample size. The results are then extended for the use of multi-auxiliary information and stratified random sampling. We consider the problem of estimating the average total family income in the US in the presence of known auxiliary information on total income per person, age of the person, and poverty. We compute the relative efficiency of the proposed estimator over the Hansen and Hurwitz (1946) estimator through the use of large real datasets. Results are also presented for sub-populations consisting of whites, blacks, others, and two or more races in addition to considering them together in a population.     

Balanced 2m factorial designs of resolution v which allow search and estimation of one extra unknown effect, 4 ≤ m ≤ 8

In this paper, we obtain balanced resolution V plans for 2^m factorial experiments (4 ≤ m ≤ 8), which have an additional feature. Instead of assuming that the three factor and higher order effects are all zero, we assume that there is at most one nonnegligible effect among them; however, we do not know which particular effect is nonnegligible. The problem is to search which effect is non-negligible and to estimate it, along with estimating the main effects and two factor interactions etc., as in an ordinary resolution V design. For every value of N (the number of treatments) within a certain practical range, we present a design using which the search and estimation can be carried out. (Of course, as in all statistical problems, the probability of correct search will depend upon the size of “error” or “noise” present in the observations. However, the designs obtained are such that, at least in the noiseless case, this probability equals 1.) It is found that many of these designs are identical with optimal balanced resolution V designs obtained earlier in the work of Srivastava and Chopra.     

Nonparametric testing for simple regression under progressive censoring with stagering entry and random withdrawal

In the context of (multi-center) clinical trials and life testins problems, a general model incorporating both the staggering entry and random withdrawal and pertaining to a simple regression problem (including the two-sample location problem as a special case) is conceived, and, within this framework, a scheme allowing progressive censoring (continuous monitoring of experimentation from the beginning) is developed along with the proposal for and study of some nonparametric testing procedures, The proposed tests rest on the construction of certain two-dimensional time-parameter stochastic processes from a triangular array of progressively censored linear rank statistics and their weak convergence to appropriate Gaussian functions. Asymptotic properties of these procedures are studied. A computer program pertaining to the numerical computations and practical administrations of these testing procedures is also provided at the end.