Comparison of nonparametric estimates of the survival functions

Abstract

The article compares three types of estimates: exponential, multiplying and power structures for the survival function of three random censoring observations on the right. It was previously established that all these three estimates are equivalent with a growing sample size, i.e. three with the same centering and normalization converge to the same Gaussian process. For specific samples, it is shown that power estimates are defined on the entire line, in contrast to exponential and multiply estimates. Therefore, power estimates are better than the other two. Censored data is used in survival analyses, biomedical trials, and industrial experiments. There are several censoring schemes (right, left, both sides, combined with competing risks, and others). However, right-sided random censoring is common in the statistical literature because it is easy to describe from a methodological point of view. Here we also consider this type of censoring, to compare our results with others.