Bias reduction in nonparametric hazard rate estimation

Abstract

The need of improvement of the bias rate of convergence of traditional nonparametric hazard rate estimators has been widely discussed in the literature. Initiated by recent developments in kernel density estimation we distinguish and extend three popular bias reduction methods to the hazard rate case. A usual problem of fixed kernel hazard rate estimates is their poor performance at endpoints. Noticing the automatic boundary adaptive property of the local linear smoother (Fan and Gijbels [13]) we adapt the method to the hazard rate case and we show that it results in estimators with bias at endpoints reduced to the level of interior bias. We then turn our attention to global bias problems. Utilizing the proposals of Hall and Marron [16] for estimation using location varying bandwidth as a means to improve the bias rate of convergence, we extend two distinct hazard rate estimators to the point that they make use of the method. The theoretical study of the resulting estimators verifies this improvement. A somewhat related way of improvement over the ordinary kernel estimates of the hazard rate is attained by extending the method of empirical transformations (Ruppert and Cline [35]). Studying the asymptotic square error of the resulting estimator we show that the advance is similar to the variable bandwidth approach. In summarizing the thesis, ideas and plans for further work are suggested