Mathematical Sciences: RUI: Partition Study for Successive Difference Analysis

这项研究旨在解决一个棘手的问题，即分析来自重复进行但不是定期进行的测量或观察的数据。提出了一种采用逐次差分的新方法作为分析的基础，假设在不同长度的区间内分段线性。要研究的问题是如何决定在哪里细分时间间隔。分析随着时间推移反复收集的数据的传统方法是为了回答金融界提出的问题。财务数据不会丢失，可以定期固定时间间隔收集。由于推动这一子领域早期发展的数据中可用的结构，这些分析方法中内置了固定和僵硬的数据结构的假设。然而，在许多研究领域，不能像在衡量美元和美分时那样，按照固定的时间表收集数据。需要全新的分析方法来获得此类数据的有效工具，因为根据非常特别的分析程序得出的结论和作出的决定都是如此。这项研究的目的是建立一个对科学调查的一般框架有效的统计理论。

This research is to attack the thorny problem of analyzing data that comes from measurements made, or observed, repeatedly but not regularly over time. A novel approach using successive differences is proposed as the basis for analysis assuming piece- wise linearity in the interval of varying lengths. The question to be studied is how to decide where to subdivide the time interval. The traditional methods for analyzing data which is collected repeatedly over time were developed to answer questions posed by the financial community. Financial data is not missing and can be collected at regular fixed time intervals. Because of the structure available in the data driving the early developments in this subfield, the assumptions of a fixed and rigid data structure is built into these analytic approaches. In many fields of research, however, data cannot be collected according to a fixed time schedule as can be done when measuring dollars and cents. Radically new methods of analysis are needed to obtain valid tools for such data, in as much as conclusions are being drawn and decisions based on results from very ad hoc analytical procedures. This research aims to work toward a statistical theory that will be valid for this general framework of scientific investigation.