On Estimation of the Intensity Density Function of a Poisson Random Field Outside the Observation Region

Abstract

A Poisson random field with intensity density function $$ \frac{\leftthreetimes (x)}{\varepsilon } $$ is observed in a bounded region G ⊆ ℝ d . It is supposed that the unknown function ⋋ belongs to a known class of entire functions. The parameter e is supposed to be known. The problem is to estimate the value ⋋(x) at the points x /∉ G. An asymptotic setup of the problem as e → 0 is considered. Bibliography: 13 titles.