  In the random-effects model of meta-analysis a canonical representation of
the restricted likelihood function is obtained. This representation relates the
mean effect and the heterogeneity variance estimation problems. An explicit
form of the variance of weighted means statistics determined by means of a
quadratic form is found. The behavior of the mean squared error for large
heterogeneity variance is elucidated. It is noted that the sample mean is not
admissible nor minimax under a natural risk function for the number of studies
exceeding three.
