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Infill asymptotics for adaptive kernel estimators of spatial intensity
Author(s) -
van Lieshout M.N.M.
Publication year - 2021
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12319
Subject(s) - mathematics , estimator , simple (philosophy) , point process , kernel (algebra) , euclidean space , intensity (physics) , variance (accounting) , mathematical analysis , statistics , combinatorics , philosophy , physics , epistemology , quantum mechanics , accounting , business
Summary 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.