Markovian interval processes I: Nonparametric inference

Consider a p-variate counting process N = (...) with jump times {...}. Suppose that the intensity of jumps ... of ... at time t depends on the other components, i. e. ..., where the ... are unknown, nonrandom functions. From observing one single trajectory of the processes N over an increasing interval of time we estimate nonparametrically the functions ... The estimators are shown to be uniformly consistent over compact sets. We derive a nonparametric asymptotic test for the hypothesis that ... does not depend on ... i. e. that ... is a renewal process. In Part II the results obtained are applied in the analysis of simultaneous neuronal spike train series.