When the mean square distortion measure is used, asymptotically optimal quantizers of uniform bivariate random vectors correspond to the centers of regular hexagons (Newman, 1982), and if the random vector is non-uniform, asymptotically optimal quantizers are the centers of piecewise regular...

A random process X(t), t[epsilon][0,1], is sampled at a finite number of appropriately designed points. On the basis of these observations, we estimate the values of the process at the unsampled points and we measure the performance by an integrated mean square error. We consider the case where...

The problems of designing the efficient sampling designs for estimation of random fields by piecewise constant estimators are studied, which is done asymptotically, namely, as the sample size goes to infinity. The performance of sampling designs is measured by the integrated mean-square error....