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Asymptotic properties of minimum contrast estimators for parameters of Boolean models. (English) Zbl 0786.62038

P. J. Diggle [Biometrics 37, 531-539 (1981)] determined in a particular Boolean model point estimators of the unknown parameters by minimizing the integrated squared distance between the true and the estimated contact distribution function. In the present paper the author establishes a rather general method for obtaining strongly consistent estimators of parameters of stationary ergodic random closed sets. In the most relevant and comparatively simple case of Boolean models these estimators are shown to be normally distributed.

MSC:

62F12 Asymptotic properties of parametric estimators
62F10 Point estimation
62G30 Order statistics; empirical distribution functions
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References:

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