Grant: Discovery Grants Program - Individual

A change point refers to a location or time at which observations or data obey two different models: before and after. Statistical studies of change-point problems date back to Page (1955) and have flourished especially since the 1980s. These studies have found applications in a wide range of areas, including quality control, finance, environmetrics, medicine, genetics and geography. An essential part of this proposed research program is to develop fast and accurate methods for change-point detection. A promising method for tackling the multiple change-point problem is to convert it to the variable selection problem by segmenting the data sequence properly. Thus, a connection between the two problems is established, and a framework is proposed to tackle multiple change point detection via the following two key steps: (1) apply the recent advances in consistent variable selection methods to detect change points; (2) employ a refined procedure to improve the accuracy of change-point estimation. The first part of this proposed research program is to continue the investigation of variable selection methods in large and complex data sets, to develop fast and efficient algorithms implemented using the statistical computing software R, and to establish statistical theory to support the developed algorithms. Second, in order to accurately refine the location of the change-point, a saddlepoint approximation will be applied to the distribution function of the test statistic, in the form of a weighted double partial sum. The approximation is very accurate and does not require the use of simulations or approximation using the Brownian bridge. Third, graph-based weighted double partial sum statistics for testing change-points will be proposed, utilizing similarity graphs and minimum spanning tree representations. This approach is motivated by the study of high-throughput data, where the dimension of each observation can be larger than the length of the sequence. This proposal seeks funding to carry out a systematic study of relationships between change-point detection and variable selection, to develop accurate saddlepoint approximations, and to explore applications in many fields. The fundamental statistical theory developed in this research program will improve our understanding of multiple change-point detection significantly and point the way towards developing new test statistics for high-dimensional data collected in many areas of science, including high-throughput genetics, environmetrics, seismic exploration, and finance.