2021/11/13 by Sudheesh, K. K., Anjana Anjana +5
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2111.07152
openalex publication_date 2021/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The analysis left truncated and right censored data is very common in survival and reliability analysis. In lifetime studies patients often subject to left truncation in addition to right censoring. For example, in bone marrow transplant studies based on International Bone Marrow Transplant Registry (IBMTR), the patients who die while waiting for the transplants will not be reported to the IBMTR. In this paper, we develop novel U-statistics under left truncation and right censoring. We prove the √(n)-consistency of the proposed U-statistics. We derive the asymptotic distribution of the U-statistics using counting process technique. As an application of the U-statistics, we develop a simple non-parametric test for testing the independence between time to failure and cause of failure in competing risks when the observations are subject to left truncation and right censoring. The finite sample performance of the proposed test is evaluated through Monte Carlo simulation study. Finally we illustrate our test procedure using lifetime data of transformers.