CURRENT STATUS DATA WITH COMPETING RISKS: LIMITING DISTRIBUTION OF THE MLE.

Area of Science:

• Statistics
• Survival Analysis
• Biostatistics

Background:

• Current status data with competing risks presents unique statistical challenges.
• Nonparametric estimation methods are crucial for analyzing such data without strong distributional assumptions.
• Existing research established n(1/3) convergence rates for both naive and MLE estimators.

Purpose of the Study:

• To derive the local limiting distributions for naive and nonparametric maximum likelihood estimators (MLE) in the context of competing risks.
• To compare the finite and asymptotic performance of these estimators.
• To introduce a novel self-induced limiting process for the MLE.

Main Methods:

• Leveraging established n(1/3) global and local convergence rates.
• Deriving local limiting distributions for both estimator types.
• Utilizing convex minorants of correlated Brownian motion processes for the naive estimator.
• Developing a new self-induced limiting process for the MLE.

Main Results:

• The local limiting distribution of the naive estimator is characterized by slopes of convex minorants of correlated Brownian motion processes.
• The local limiting distribution of the MLE is described by a novel self-induced limiting process.
• Simulation studies confirm the MLE's superiority over the naive estimator in mean squared error.

Conclusions:

• The nonparametric maximum likelihood estimator (MLE) is more effective than the naive estimator for current status data with competing risks.
• The MLE exhibits better mean squared error performance across various sample sizes.
• The derived limiting distributions provide theoretical underpinnings for estimator selection.