Moments of the Product-Limit Estimator Under Left-Truncation and Right-Censoring
ABSTRACT The product-limit estimator (PLE) is a well-known nonparametric estimator for the distribution function of the lifetime when data are left-truncated and right-censored. Much work has focused on developing its asymptotic properties. Finite sample results have been difficult to obtain. This article is concerned about finite moments of the PLE. The moments of the PLE can be represented as a power series in n −1. In addition, through the U-statistic mechanism, we obtain also computable formulas for the first, second, third, and fourth of the PLE up to o(n −2). Finally, a numerical example is presented.