We apply the Abramson principle to define adaptive kernel estimators for the intensity function of a spatial point process. We derive asymptotic expansions for the bias and variance under the regime that n independent copies of a simple point process in Euclidean space are superposed. The method is illustrated by means of a simple example and applied to tornado data.

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Australian and New Zealand Journal of Statistics
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

van Lieshout, M.N.M. (2021). Infill asymptotics for adaptive kernel estimators of spatial intensity. Australian and New Zealand Journal of Statistics, 63(1), 159–181. doi:10.1111/anzs.12319