Abstract
A Poisson process on metric space is introduced and some of the properties of the stochastic integral with respect to this process are described. This integral allows us to define the likelihood ratio formula and to derive certain useful inequalities for the moments of likelihood ratio. Supposing that the intensity function of the Poisson process depends on the unknown finite-dimensional parameter, we define the maximum likelihood, Bayes, and minimum distance estimators of this parameter and give the first examples of these estimators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kutoyants, Y.A. (1998). Auxiliary Results. In: Statistical Inference for Spatial Poisson Processes. Lecture Notes in Statistics, vol 134. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1706-0_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1706-0_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98562-6
Online ISBN: 978-1-4612-1706-0
eBook Packages: Springer Book Archive