Data-Based Nonparametric Estimation of the Hazard Function with Applications to Model Diagnostics and Exploratory Analysis
Two general classes of nonparametric kernel estimators of the hazard function are introduced, which include both a 1-parameter estimator and a more complex 3-parameter estimator. In addition, employing the idea of cross-validation, the authors present a data-based algorithm for smoothing parameter selection. The article compares the data-based 1and 3-parameter estimators in a simulation experiment to the maximum likelihood estimator assuming the correct failure distribution and censoring mechanism. The 3-parameter estimator is found to perform well over a wide range of settings. On the average, the estimator recovers the shape of the underlying failure hazard and is competitive with the parametric estimator over a subset of the positive half line. Two examples illustrate possible uses of the nonparametric estimators.