Summary
We consider nonparametric estimation of hazard functions and their derivatives under random censorship, based on kernel smoothing of the Nelson (1972) estimator. One critically important ingredient for smoothing methods is the choice of an appropriate bandwidth. Since local variance of these estimates depends on the point where the hazard function is estimated and the bandwidth determines the trade-off between local variance and local bias, data-based local bandwidth choice is proposed. A general principle for obtaining asymptotically efficient data-based local bandwiths, is obtained by means of weak convergence of a local bandwidth process to a Gaussian limit process. Several specific asymptotically efficient bandwidth estimators are discussed. We propose in particular an, asymptotically efficient method derived from direct pilot estimators of the hazard function and of the local mean squared error. This bandwidth choice method has practical advantages and is also of interest in the uncensored case as well as for density estimation.
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Research supported by UC Davis Faculty Research Grant and by Air Force grant AFOSR-89-0386
Research supported by Air Force grant AFOSR-89-0386
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Müller, HG., Wang, JL. Locally adaptive hazard smoothing. Probab. Th. Rel. Fields 85, 523–538 (1990). https://doi.org/10.1007/BF01203169
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DOI: https://doi.org/10.1007/BF01203169