Asymptotic properties of minimum contrast estimators for parameters of boolean models

Summary This paper presents a method for the estimation of parameters of random closed sets (racs’s) in ℝ ^d based on a single realization within a (large) convex sampling window. The essential idea first applied by Diggle (1981) in a special case consists in defining the estimation by minimizing a suitably defined distance (called contrast function) between the true and the empirical contact distribution function of the racs under consideration, where the most relevant case of Boolean models is discussed in details. The resulting estimates are shown to be strongly consistent (if the racs is ergodic) and asymptotically normal (if the racs is Boolean) when the sampling window expands unboundedly.