V. K. Klonias
Published: 1985
Total Pages: 28
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Estimators for the probability density function, cumulative distribution function, and hazard function are proposed in the random censorship setting. The estimators are derived from the Kaplan-Meier product limit estimator by maximum penalized likelihood methods. The authors establish the existence and uniqueness of the estimates, which are exponential splines with knots at the uncensored observations, and provide an efficient algorithm for their numerical evaluation. They prove the consistency, in probability and almost surely, of the density estimates in the Hellinger distance, the L sub p norms for p =1, 2, infinity, and the Sobolev norm. The corresponding hazard rate estimator converges uniformly on bounded intervals. (Author).