Nearest neighbor analysis of point processes: Applications to multidimensional scaling

A new approach for evaluating spatial statistical models based on the (random) number 0 ≤ N(i, n) ≤ n of points whose nearest neighbor is i in an ensemble of n + 1 points is discussed. The second moment of N(i, n) offers a measure of the centrality of the ensemble. The asymptotic distribution of N(i, n) and the expected degree of centrality for several spatial and nonspatial point processes is described. The use of centrality as a diagnostic statistic for multidimensional scaling is explored.