Local polynomial smoothing based on the Kaplan–Meier estimate

Abstract

The local polynomial modeling of the Kaplan–Meier estimate for random designs under the right censored data setting is investigated in detail. Two classes of boundary aware estimates are developed: estimates of the distribution function and its derivatives of any arbitrary order and estimates of integrated distribution function derivative products. Their statistical properties are quantified analytically and their implementation is facilitated by the development of corresponding data driven plug-in bandwidth selectors. The asymptotic rate of convergence of the plug-in rule for the estimates of the distribution function and its derivatives is quantified analytically. Numerical evidence is also provided on its finite sample performance. A real life data analysis illustrates how the methodological advances proposed herein help to generate additional insights in comparison to existing methods.