On the estimation of poles in intensity functions

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.