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Statistica Sinica 5(1995), 221-234



Michael L. Stein

University of Chicago

Abstract: The standard asymptotic regime for studying the properties of estimators of the reduced second moment function K(t) of a spatial point process is to fix the law of the process and t and let the observation region grow. No results comparing the asymptotic variability of these estimators are available for processes other than Poisson. This paper obtains asymptotic results for a large class of stationary point processes by using a different asymptotic regime. Specifically, the distance t at which K is to be estimated is allowed to grow with the observation region. Using this asymptotic setup, it is shown that using the notion of projection of a U-statistic leads to estimators that converge to the truth at a faster rate than standard estimators not using this projection idea.

Key words and phrases: Edge effects, interpoint distance distribution, reduced second moment function, U-statistics.

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