Consistency of the Generalized MLE with Interval-Censored and Masked Competing Risks Data

Abstract

We consider nonparametric estimation based on interval-censored competing risks data with masked failure cause. The generalized maximum likelihood estimator of the joint survival function of the failure time and the failure cause is studied under mixed case interval censorship and random partition masking. Strong consistency in the L ₁(μ)-topology is established for some finite measure μ which is derived from the joint censoring and masking distribution. Under additional regularity assumptions we also establish the strong consistencies in the topologies of weak convergence, point-wise convergence, and uniform convergence.

Keywords:

• Identifiability
• Mixed case interval censoring
• Random partition masking

Mathematics Subject Classification:

• Primary 62G05
• Secondary 62G20

Acknowledgment

The authors thank the Editor, an Associate Edtior and the referees for invaluable comments.