Optimality of balanced uniform repeated measurements designs. (English) Zbl 0544.62068

Kunert, Joachim

Ann. Stat. 12, 1006-1017 (1984).

The experiment of a repeated measurements design is based on n experimental units, t treatments and p periods and is denoted by \(\Omega_{t,n,p}\). It is shown that:
i) If \(t=n=p\neq 2\) and if a balanced Latin square exists, this is universally optimal for the estimation of direct effects over \(\Omega_{t,t,t}\). ii) A balanced uniform design is universally optimal for the estimation of direct effects over \(\Omega_{t,2t,t}\) for \(t\geq 6.\)
iii) If \(t=n=p\) and a design with given properties exists, then no balanced Latin square design can be universally optimal for the estimation of residual effects. Such an example is presented. iv) If \(n=t(t-1)\) an orthogonal residual effects design is universally optimal for the estimation of residual effects over \(\Omega_{t,n,t}\).

Reviewer: S.Kounias

MSC:

62K05	Optimal statistical designs
62K10	Statistical block designs
62P10	Applications of statistics to biology and medical sciences; meta analysis

Keywords:

linear model; universal optimality; projection matrix; generalized inverse; repeated measurements design; balanced Latin square; estimation of direct effects; balanced uniform design; orthogonal residual effects design