Corner kicks are an important event in soccer because they are often the result of strong attacking play and can be of keen interest to sports fans and bettors. Peng, Hu, and Swartz (2024, Computational Statistics) formulate the mixture feature of corner kick times caused by previous corner kicks, frame the commonly available corner kick data as right-censored event times, and explore patterns of corner kicks. This paper extends their modeling to accommodate the potential correlations between corner kicks by the same teams within the same games. We con- sider a frailty model for event times and apply the Monte Carlo Expec- tation Maximization (MCEM) algorithm to obtain the maximum like- lihood estimates for the model parameters. We compare the proposed model with the model in Peng, Hu, and Swartz (2024) using likelihood ratio tests. The 2019 Chinese Super League (CSL) data are employed throughout the paper for motivation and illustration.

翻译：角球是足球比赛中的重要事件，因其常由强力进攻引发，并受到体育爱好者与博彩者的密切关注。Peng、Hu与Swartz（2024，《计算统计学》）针对先前角球引发的角球时间混合特征进行建模，将常见的角球数据构建为右删失事件时间，并深入探究角球的发生规律。本文扩展了他们的模型，以处理同一场比赛中同一球队角球之间可能存在的相关性。我们构建了事件时间的脆弱模型，并采用蒙特卡洛期望最大化（MCEM）算法获取模型参数的最大似然估计。通过似然比检验，我们将所提模型与Peng、Hu及Swartz（2024）的模型进行比较。全文以2019年中国足球协会超级联赛（CSL）数据作为研究动机与实证案例。