Nonparametric Inference for Rates with Censored Survival Data

This paper concerns nonparametric inference for hazard rates with censored serial data. The focus is upon "delta sequence" estimators of the form hₙ(x) = ∫ Kb(x, y) dHₙ(y) with Kb integrating to 1 and concentrating mass near x as b → 0. Hₙ is the Nelson-Aalen empirical cumulative hazard. Strong approximation and simultaneous confidence bands are derived for Rosenblatt-Parzen estimators, with Kb(x, y) = w((x - y)/b)/b, b = o(n⁻¹), and w(·) a well-behaved density. This work generalizes global deviation and mean square deviation results of Bickel and Rosenblatt and others to censored survival data. Simulations with exponential survival and censoring indicate the effect of censoring on bias, variance, and maximal absolute deviation. Data from a survival experiment with serial sacrifice are analysed.