Optimal sampling design under a spatial correlation model

Abstract

Lawry and Bellhouse (J. Statist. Plann. Inference 32 (1992) 385–399) showed when the optimal sampling design exists and when it does not exist under a class of spatial correlation models where a sample of size N with equal inclusion probabilities for all units is taken from an N× N array. In this article, their work is extended to an N× M array with any sample size n. When the inclusion probabilities are 1 2 , 1 3 and 1 5 the optimal sampling designs exist for any N× M array. The optimal designs for inclusion probabilities 1 2 and 1 3 are systematic Latin square sampling designs and for inclusion probabilities 1 5 is systematic knight's move Latin square sampling design. The optimal sampling design exists for a 2× M array with any inclusion probability. For other cases the optimal sampling designs does not exist.