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 misspecification 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.