Fast Computation of Fully Automated Log-Density and Log-Hazard Estimators

The computation of fully automated or data-driven penalized likelihood estimators of logarithmic densities and hazards is accomplished using B-spline approximants. The banded structure induced by B-splines gives rise to very fast and statistically effective algorithms. Automation is achieved using one-step Newton–Raphson cross-validation scores which are simplified to forms reminiscent of AIC criteria. The cost of computing these scores is linear in the number of data points. Approximate Bayesian confidence intervals are also derived and illustrated with some examples. Such intervals provide a valuable aid to the interpretation of estimated curves. The small sample performance (bias and variability) of the estimators is investigated by a simulation study.