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

Resumo

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 ε 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 ε → 0 is considered. Bibliography: 13 titles.