Semiparametric smoothing approach to hazard rate estimation

This research extends the multiplicative density estimation technique of Naito [(2004), ‘Semiparametric Density Estimation by Local $ L_2 $ L2-fitting’, The Annals of Statistics, 32, 1162–1191] to the hazard rate setting. The proposed estimate consists of a parametric estimate of the underlying model times a nonparametric correction factor. The reasoning of this approach is first illustrated by varying the shape parameter involved in the approximation and displaying the benefits of the resulting estimate in an $ L_2 $ L2 sense for specific example distributions. The sample analogue of this approach is then used as the basis for building an estimator of the true hazard rate function. Establishing its asymptotic properties and specifically its mean square error, reveals that the suggested estimate performs better than its nonparametric counterpart. Detailed instructions are given for calculating the operational characteristics of the estimate, that is, its shape parameter and bandwidth. Finally, its practical performance is illustrated for simulated as well as a real world data example.