讲座主题: Estimating the Inter-Occurrence Time Distribution From Superposed Renewal Processes

主讲人：叶志盛

讲座时间：2021-5-20（周四）9:30-10:30

地点：综合楼644

主讲人简介：    

Dr. Ye received a joint B.E. (2008) in Material Science & Engineering, and Economics from Tsinghua University. He received a Ph.D. degree from National University of Singapore. He is currently an Associate Professor in the Department of Industrial Systems Engineering & Management at National University of Singapore. His research areas include data-driven decision analysis, degradation data anlyais, lifetime and recurrence data analysis, and reliability modeling.

讲座摘要：

Superposition of renewal processes is common in practice, and it is challenging to estimate the distribution of the individual inter-occurrence time associated with the renewal process. This is because with only aggregated event history, the link between the observed recurrence times and the respective renewal processes are completely missing, rendering inapplicability of existing theory and methods. In this talk, we propose a nonparametric procedure to estimate the inter-occurrence time distribution by properly deconvoluting the renewal equation with the empirical renewal function. By carefully controlling the discretization errors and properly handling challenges due to implicit and non-smooth mapping via the renewal equation, our theoretical analysis establishes the consistency and asymptotic normality of the nonparametric estimators. The proposed nonparametric distribution estimators are then utilized for developing theoretically valid and computationally efficient inferences when a parametric family is assumed for the individual renewal process. Comprehensive simulations show that compared with the existing maximum likelihood method, the proposed parametric estimation procedure is much faster, and the proposed estimators are more robust to round-off errors in the observed data.