FITTING CONTINUOUS PIECEWISE LINEAR POISSON INTENSITIES VIA MAXIMUM LIKELIHOOD AND LEAST SQUARES

We investigate maximum likelihood (ML) and ordinary least squares (OLS) methods to fit a continuous piecewise linear (PL) intensity function for non-homogeneous Poisson processes. The estimation procedures are formulated as convex optimization problems that are highly tractable. We also study the model mis-specification issues in settings where the point process is non-Poisson or the underlying intensity is not piecewise linear. The performances of ML and OLS estimators are exhibited through a computational study, with both simulated data and real data from a large U.S. bank call center.