Probability Seminar Cornelia Wichelhaus (TU Darmstadt)

Nonparametric Estimation in Stochastic Networks

Cornelia's research interests are on the intersection of (nonparametric) statistics and stochastic networks.

Nonparametric Estimation in Stochastic Networks  Stochastic networks are interacting systems of nodes with service  stations between which customers move in order to receive service.  The  talk addresses nonparametric estimation problems for these systems in  discrete time. In particular we are interested in estimating the service  time distributions at the nodes based on incomplete observations of the  systems. We assume that we are only able to observe the external  arrivals and departures of customers. We propose two estimation  approaches. The first one is based on the construction of a so-called  sequence of differences and the second utilizes the structure of  cross-covariance functions between specific stochastic processes of the  network.  Both methods lead to deconvolution problems which we solve  explicitly and which lead to consistent estimators. As main properties  we show functional central limit theorems for the estimators in  appropriate discrete spaces.