Extreme Long-Term Survival Probabilities Estimation in Highly Censored Data

• Grant number: 25/22925-3
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: February 01, 2026
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Antonio Carlos Pedroso de Lima
• Grantee: Eduardo Janotti Cavalcante
• Supervisor: Ligia Carla Pinto Henriques Jorge Rodrigues
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Universidade de Lisboa, Portugal
• Associated to the scholarship: 25/10342-3 - Extreme Long-Term Survival Probabilities Estimation in Highly Censored Data, BP.DD

Abstract

Extreme Value Theory plays an important role in modeling rare events, particularly through thePeaks-Over-Threshold method and the Generalized Pareto Distribution. However, traditionalapplications of these models face limitations when dealing with incomplete data (censoring)and long-term survival scenarios, where standard assumptions may not hold. Despite recentadvances, challenges remain regarding the selection of the threshold from which the Generalized Pareto distribution is valid and the integration of modern statistical methodologies. Thisresearch aims to refine and extend semi-parametric models of extreme long-term survival probabilities while minimizing restrictive assumptions and preserving flexibility. By using extremevalue theory, we aim to develop a robust framework capable of capturing distinct behaviors indifferent data regimes. The proposed methodology will aim to improve the selection of thresholds, predictive accuracy, and interpretability, with potential applications in medicine, finance,and environmental sciences. (AU)