First-passage-based boundary estimation in functional data.

Area of Science:

• Statistics
• Biostatistics
• Environmental Science

Background:

• Functional data analysis is essential for understanding dynamic processes.
• Threshold-crossing events are critical in various applications, including risk assessment.
• Accurate reconstruction of dynamic boundaries is challenging.

Purpose of the Study:

• To develop a practical estimation strategy for reconstructing time-varying functional boundaries.
• To address the challenge of identifying threshold-crossing events in population-level data.
• To distinguish between a time-varying benchmark and a conditional crossing-level curve.

Main Methods:

• Formulating boundary recovery as a first-passage identification problem.
• Employing penalized cubic B-splines for boundary representation with roughness control.
• Utilizing generalized cross-validation for tuning parameter selection.
• Applying the method to age-standardized colon cancer incidence trajectories.

Main Results:

• The proposed estimator accurately recovers various smooth threshold shapes.
• Performance improves with increased crossing information and sample size.
• The framework provides stable empirical boundary reconstructions for population data.
• The method explicitly accounts for left-censoring in observed data.

Conclusions:

• The developed method offers a robust approach for functional boundary reconstruction.
• This technique enhances understanding of risk activation triggered by threshold crossings.
• The application to cancer incidence data demonstrates practical utility and stability.