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Follow-up experiment is widely applied to various fields such as science and engineering, since it is an indispensable strategy, especially when some additional resources or information become available after the initial design of experiment is carried out. Moreover, some extra factors may be added in the follow-up experiment. One may augment the number of runs and/or factors for the purpose of application. In this paper, the issue of the uniform row augmented designs and column augmented designs with mixed two- and three-level is investigated. The uniformity of augmented designs is discussed under the Lee discrepancy, some lower bounds of Lee discrepancy for the augmented designs are obtained. The construction algorithm of the uniform augmented designs is given. Some numerical examples indicate that uniform augmented designs can be constructed with high efficiency. [ABSTRACT FROM AUTHOR]

We consider an exact factor model with integrated factors and propose an LM-type test for unit roots in the idiosyncratic component. We show that, for a fixed number of panel individuals (N) and when the number of time points (T) tends to infinity, the limiting distribution of the LM-type statistic is a weighted sum of independent Chi-square variables with one degree of freedom, and whenTtends to infinity followed byNtending to infinity, the limiting distribution is standard normal. The results should contribute to the challenging task of deriving likelihood-based unit-root tests in dynamic factor models. [ABSTRACT FROM AUTHOR]

In this article, we consider experimental situations in which m two-lever factors are to be studied using a two-level main effects plan involving n runs which are partitioned into b blocks of size k = n/b. For the casen ≡ 1(mod 4) and b ≤ k, we derive some new methods of constructing E-optimal designswhich tend to be highly efficient under other optimality criteria as well. [ABSTRACT FROM AUTHOR]