On Statistical Analysis of Competing Risks with Application to the Time of First Goal
Abstract: The contribution deals with the analysis and application of the competing risks model. First, the problem of identifiability of marginal and joint distributions of competing random variables is discussed. Then, the notion of copula is recalled and used to express the dependence in the competing risks scheme. Copula model is then utilized to the analysis of times of scoring the first goal in a football (soccer) match. It is assumed that competing latent times are exponentially distributed with parameters depending on attack and defence strengths of teams, while their mutual dependence is described with the aid of a conveniently chosen copula ensuring the model identifiability. As a real example the data from the season 2014-2015 of the Czech premier league (called Synot League) are analyzed. It is shown that the correlation in the framework of proposed model is, as a rule, negative, and its value is related to the first goal importance. The outcomes of analysis are discussed both from theoretical and practical point of view.
Keywords: survival analysis, competing risks, copula, sports statistics.
Pages: 606 – 623 | Full PDF Paper