NON-PARAMETRIC INFERENCE FOR RATES AND DENSITIES WITH CENSORED SERIAL DATA

This thesis concerns non-parametric inference for density and

rate functions with censored serial data. The focus is upon "delta sequence" curve estimators of the form a(,n)(x) = (' )(, ) K(,m)(x,y)dA(,n)(y) with K(,m) integrating to 1 and concentrating mass near x as m(--->)(INFIN). Typically, A(,n) is either the Kaplan-Meier product-limit estimator of the cumulative distribution or the Nelson-Aalen empirical cumulative rate. Bias, covariance, expected mean square error convergence, and uniform consistency are presented. Asymptotic normality and simultaneous confidence bands are derived for Rosenblatt-Parzen estimators, with K(,m)(x,y) = mw(m(x-y)), m = o(n), and w(.) a well-behaved density. This work generalizes global deviation and mean square deviation results of Bickel and Rosenblatt, and others to censored serial data. Simulations with exponential survival and censoring indicate the effect of censoring on bias, variance, and maximal absolute deviation. Results extend to a multiple decrement/competing risks model. Death rates and sacrifice frequencies are analysed with data from a survival experiment with serial sacrifice.