報告題目：Estimating the Inter-Occurrence Time Distribution From Superposed Renewal Processes
報 告 人：葉志盛 新加坡國立大學 副教授
報告時間：2021年3月31日 下午 16:00-17:00
報告地點：騰訊會議
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會議 ID：514 302 527
校内聯系人：趙世舜 zhaoss@jlu.edu.cn
報告摘要：
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.
報告人簡介：
葉志盛副教授于2008年獲得清華大學材料科學與工程、經濟學雙學士學位，博士畢業于新加坡國立大學。現任新加坡國立大學工業系統工程與管理系副教授。葉教授的主要研究方向包括應用概率、統計相依模型、退化分析、可靠性建模以及随機管理等。在Technometrics，Journal of Quality Technology，Naval Research Logistics，IEEE Transactions on Reliability等國際知名期刊上發表高水平論文60餘篇。
