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Biometrika 2000 87(2):265-283; doi:10.1093/biomet/87.2.265
© 2000 by Biometrika Trust
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Smoothing techniques and estimation methods for nonstationary Boolean models with applications to coverage processes

IS MolchanovA1 and SN ChiuA2

A1 Department of Statistics, University of Glasgow, Glasgow G12 8QW, UK E-mail: ilya@stats.gla.ac.uk A2 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, PRC E-mail: snchiu@math.hkbu.edu.hk

Kernel smoothing methods are applied to nonparametric estimation for nonstationary Boolean models. In many applications only exposed tangent points of the models are observable rather than full realisations. Several methods are developed for estimating the distribution of the underlying Boolean model from observation of the exposed tangent points. In particular, estimation methods for coverage processes are studied in detail and applied to neurobiological data.

Key Words: coverage; Johnson-Mehl model; Kernel smoothing; nonstationary Boolean model


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