Semi-parametric Inference for Regression Models Based on Marked Point Processes

Introduction and Basic Definitions The monography by Andersen et al. (1993) presents a kind of canonical approach to the statistical analysis of point process models. It deals with multivariate point processes where each random event carries information on the occurrence time and the type of event, the latter being from a finite set E of alternatives. The theoretical fundament to multivariate point processes was laid - among others - by Jacod (1975), Bremaud (1981) and Dellacherie & Meyer (1982). There are applications, however, where an uncountable set E (e.g., E the set of real numbers) of alternatives - now called marks - is more appropriate, see Scheike (1994a,b), Murphy (1995) and Pruscha (1997). A mathematical foundation of marked point processes (MPP's) is given by Last and Brandt (1995), but this work does not contain all tools necessary for statistical analysis. The first goal of the present paper is to fill this gap. W