Fixed design local polynomial smoothing and bandwidth selection for right censored data

Abstract

The local polynomial smoothing of the Kaplan–Meier estimate for fixed designs is explored and analyzed. The first benefit, in comparison to classical convolution kernel smoothing, is the development of boundary aware estimates of the distribution function, its derivatives and integrated derivative products of any arbitrary order. The advancements proceed by developing asymptotic mean integrated square error optimal solve-the-equation plug-in bandwidth selectors for the estimates of the distribution function and its derivatives, and as a byproduct, a mean square error optimal bandwidth rule for integrated derivative products. The asymptotic properties of all methodological contributions are quantified analytically and discussed in detail. Three real data analyses illustrate the benefits of the proposed methodology in practice. Finally, numerical evidence is provided on the finite sample performance of the proposed technique with reference to benchmark estimates.