On Estimating Threshold Crossing Times

• Activity Number: 309
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Tony Sit*+ and Victor de la Pena and Mark Brown
• Companies: Columbia University and Columbia University and The City University of New York
• Keywords: First-hitting time ; Threshold-crossing ; Probability bounds ; Decopuling ; Climate change ; Renewal theory

Abstract

Given a range of future projected climate trajectories that represent the future climate condition, an unbiased estimator for the threshold-crossing time will be the mean of the crossing-times of all the simulated paths. This estimator, however, can provide a sensible estimation only when all the simulated paths have infinite/observed first-hitting times. In this paper, we propose remedies to the estimation problem to deal with situations in which there is one or more simulated paths having a right censored boundary crossing time. This extends the results in Section 2.7 of de la Pena (1997) and provides a universal sharp lower bound than what is shown in de la Pena and Yang (2004). Two examples of applications of the bounds derived are provided: one involving the growth of cancer tumours and the other one deals with drought prediction in US Southwest and Mediterranean region based on the data calculated from IPCC Fourth Assessment (AR4) model simulations of the twentieth and twenty-first centuries.