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Biometrika 2000 87(2):251-263; doi:10.1093/biomet/87.2.251
© 2000 by Biometrika Trust
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On the estimation of poles in intensity functions

E Choi and P Hall

Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia E-mail: choi@maths.anu.edu.au; peter.hall@anu.edu.au

Motivated by spatial data on earthquake epicentres, we consider the problem of estimating properties of poles in point-process intensity functions. Our methods are semiparametric, requiring only 'asymptotic' models for the intensity. They produce estimates of the locations and strengths of poles. Strength is expressed in terms of an exponent of regular variation, and is simply related to the correlation dimension of the underlying point process. It is argued that existing methods for estimating pole strength are restrictive in terms of the range of strengths that they allow.

Key Words: correlation dimension; density estimation; earthquake; epicentre; extreme value theory; fractal; Japan; point process; Poisson process; regular variation; seismic; spatial statistics


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