This paper considers the problem of constructing optimal approximate designs when an independent variable might be censored. The problem is which design should be applied in practice to obtain the best approximate design when a censoring distribution is assumed known in advance. The approach for finite or continuous design spaces deserves different attention. In both cases, equivalent theorems and algorithms are provided in order to calculate optimal designs. Some examples illustrate this approach for D-optimality. [ABSTRACT FROM AUTHOR]
In this paper, testing procedures based on double-sampling are proposed that yield gains in terms of power for the tests of General Linear Hypotheses. The distribution of a test statistic, involving both the measurements of the outcome on the smaller sample and of the covariates on the wider sample, is first derived. Then, approximations are provided in order to allow for a formal comparison between the powers of double-sampling and single-sampling strategies. Furthermore, it is shown how to allocate the measurements of the outcome and the covariates in order to maximize the power of the tests for a given experimental cost. [ABSTRACT FROM AUTHOR]
The assumption that two linear statistics are identically distributed can be used to characterize various populations. This is an object of the so-called characterization theorems. But if the assumptions of the characterization theorem are fulfilled only approximately, then may we state that the conclusion of this characterization is also fulfilled approximately? Theorems, in which this kind of problems are considered, are called the stability theorems. According to Eaton's theorem, if under the additional conditions, the two linear statistics [image omitted] and [image omitted] have the same distribution as the monomial X1, then this monomial has a symmetric stable distribution of order α. The stability estimation in this theorem is investigated in the paper. [ABSTRACT FROM AUTHOR]