Edgeworth Expansion and Bootstrap Approximation for Studentized Product-Limit Estimator with Truncated and Censored Data

The product-limit estimator under left truncation and right censoring was first proposed and shown to be asymptotically normal by Tsai et al. (1987). In this article, we shall develop an Edgeworth expansion for the studentized product-limit estimator. This is achieved by representing the studentized product-limit estimator as a U-statistic plus some negligible remainder terms. The bootstrap is employed to approximate the distribution of the studentized product-limit estimator and shown to be second-order accurate.

Keywords:

• Bootstrap approximation
• Edgeworth expansion
• Left truncation
• Product-limit estimator
• Random censorship

Mathematics Subject Classification:

• Primary 62G05
• Secondary 62E20