A framework for statistical modelling of the extremes of longitudinal data, applied to elite swimming
纵向数据极端值的统计建模框架及精英游泳应用AI 解读 ↓
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纵向数据极端值的统计建模框架及精英游泳应用
- 研究问题
- 面对大量短、不规则且不同步观测的个体序列，如何刻画尾部结果、个体差异和时间依赖，并推断运动员职业生涯的极端表现？
- 方法与思路
- 作者以共同阈值以上的广义帕累托分布描述尾部，建模序列间差异、分布随时间变化及序列内依赖，并采用贝叶斯推断。
- 材料陈述的贡献
- 摘要称，框架允许渐近相关与渐近独立，并通过男子百米蛙泳数据展示对个体破纪录或次年取得最快成绩概率的推断。
- 阅读关注点
- 应核对高阈值选择、序列间独立和共同尾部分布假设，以及个体参数、时间变化与渐近依赖类型如何区分和估计。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未经核实；摘要未提供概率估计或验证结果，也不能据此推广至序列间相关的数据。
原文摘要
We develop methods, based on extreme value theory, for analysing observations in the tails of longitudinal data, i.e., a data set consisting of a large number of short time series, which are typically irregularly and non-simultaneously sampled, yet have some commonality in the structure of each series and exhibit independence between time series. Extreme value theory has not been considered previously for the unique features of longitudinal data. Across time series the data are assumed to follow a common generalised Pareto distribution, above a high threshold. To account for temporal dependence of such data we require a model to describe (i) the variation between the different time series properties, (ii) the changes in distribution over time, and (iii) the temporal dependence within each series. Our methodology has the flexibility to capture both asymptotic dependence and asymptotic independence, with this characteristic determined by the data. Bayesian inference is used given the need for inference of parameters that are unique to each time series. Our novel methodology is illustrated through the analysis of data from elite swimmers in the men's 100m breaststroke. Unlike previous analyses of personal-best data in this event, we are able to make inference about the careers of individual swimmers - such as the probability an individual will break the world record or swim the fastest time next year.