When observing the realization of a point process the question naturally arises whether this output represents a homogeneous Poisson point process or a more complicated stochastic model. Very often technical imperfections of the recording device lead to delayed registration of some or all of its point events. It is the aim of this contribution to develop statistical tests helpful to discover the presence of such delay mechanisms. Most powerful and locally most powerful tests are proposed which are useful in these regards, in particular if the period of observation of the point process is long. The fact that in many experimental set-ups the observed process of possibly delayed point events of a Poisson point process turns out to be again a Poisson point process facilitates the elaboration of such tests.

Bibliography:

Daley,D.J. & Vere-Jones,D. An introduction to the theory of point processes. Springer, New York, 1988. Gradshteyn,I.S. & Ryzhik,I.M. Table of integrals, series and products. Academic Press, New York, 1965.

Keywords: Statistical inference for point processes; Model selection; Optimal statistical tests

Biography: Franz Streit is a retired professor of statistics and applied probability of the department of mathematics of the university of Geneva. His research areas are statistical methodology, inference for point processes, geometrical stochastics and multivariate statistical analysis.