Gradual Functional Changes

逐渐的功能变化

• 批准号: 490757989
• 负责人: Professorin Dr. Claudia Kirch
• 金额: --
• 依托单位: Mathematical Institute
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/490757989?language=en
• 关键词: Gradual; Functional; Changes

With the advance of computer facilities and data storage warehouses, more and more data are being recorded continuously during a time period or intermittently at plethora of discrete time points. These are both examples of functional data, which furthermore embrace random fields or manifolds. Our attention is devoted to stochastic functions predominantly represented by random curves or surfaces, where every function is considered as a single observation. These observations are naturally ordered with respect to time and possibly changing over time. The interest is not in an individual change within each curve, but in a change of the pattern across the sequence of curves. Almost all existing change detection methods are designed to discover abrupt breaks. Little attention has been paid to smooth structural changes, which may be more realistic in practice. With the vantage of functional analysis and empirical processes, we can deploy advanced statistical tools like bootstrap or lasso to diagnose the gradual change of functional form in the time series of random curves.

随着计算机设备和数据存储仓库的进步，越来越多的数据在一段时间内连续记录或在大量离散时间点间歇记录。这两个都是函数数据的例子，它们进一步包含了随机场或流形。我们的注意力主要集中在随机函数上，随机函数主要由随机曲线或随机曲面表示，其中每个函数都被视为单个观察值。这些观察结果自然是按时间顺序排列的，并可能随时间而变化。我们感兴趣的不是每条曲线内的个别变化，而是曲线序列中模式的变化。几乎所有现有的变更检测方法都是为了发现突变而设计的。很少有人关注平稳的结构变化，这在实践中可能更为现实。利用功能分析和经验过程的优势，我们可以利用bootstrap或lasso等先进的统计工具来诊断随机曲线时间序列中功能形式的逐渐变化。