Bias in nearest-neighbor hazard estimation

Abstract

In nonparametric curve estimation, the smoothing parameter is critical for performance. In order to estimate the hazard rate, we compare nearest neighbor selectors that minimize the quadratic, the Kullback-Leibler, and the uniform loss. These measures result in a rule of thumb, a cross-validation, and a plug-in selector. A Monte Carlo simulation within the three-parameter exponentiated Weibull distribution indicates that a counter-factual normal distribution, as an input to the selector, does provide a good rule of thumb. If bias is the main concern, minimizing the uniform loss yields the best results, but at the cost of very high variability. Cross-validation has a similar bias to the rule of thumb, but also with high variability.