Estimation of Palm measures of stationary point processes

Summary Estimators of the Palm measure of a stationary point process on a finite-dimensional Euclidean space are developed and shown to be strongly uniformly consistent. From them, similarly consistent estimators of reduced moment measures, the spectral measure, the spectral density function and the underlying probability measure itself are derived. Normal and Poisson approximations to distributions of estimators are presented. Application is made to the problem of combined inference and linear state estimation.Research supported by Air Force Office of Scientific Research, AFSC, grant 82-0029C. The United States Government is authorized to reproduce and distribute reprints for governmental purposes