Robust estimation of point process intensity features using k-minimal spanning trees

Minimal spanning trees (MST) have been applied to multi-dimensional random processes for pattern recognition and randomness testing. We present a robust version of the MST to estimate complexity features of a point process intensity function under an epsilon contaminated model for the intensity. The principal feature considered is the Renyi entropy of the mixture and a strongly consistent entropy estimator is given which depends on the data only through the total length of the MST passing through the data points. Robustification of the MST estimator is achieved by applying the theory of k-minimum MST.