  We observe a realization of a stationary generalized weighted Voronoi
tessellation of the d-dimensional Euclidean space within a bounded observation
window. Given a geometric characteristic of the typical cell, we use the
minus-sampling technique to construct an unbiased estimator of the average
value of this geometric characteristic. Under mild conditions on the weights of
the cells, we establish variance asymptotics and the asymptotic normality of
the unbiased estimator as the observation window tends to the whole space.
Moreover, the weak consistency is shown for this estimator.
