Statistical analysis of Lévy driven Cox point processes - spatial and spatio-temporal

In the talk we consider the problem of parameter estimation of Lévy driven Cox point processes (i.e. Cox processes with driving field obtained by kernel smoothing of a Lévy basis). We will concentrate on the inhomogeneous case satisfying the second order inhomogeneity reweighted stationarity assumption. Then the second order moment characteristics like $g$ and $K$ function can be used for minimum contrast estimation. In the spatio-temporal case we will assume that the smoothing kernel is separable. This assumption does not imply separability of the second order moment measure of the spatio-temporal process. However it is still possible to use for the estimation the spatial and temporal projection of the original process.

The talk is based on joint work with Eva Vedel Jensen and Jiri Dvorak.