Data depth has provided a systematic nonparametric multivariate framework and given rise to a powerful multivariate analysis tool set. However, its full potential in spacings and classification is yet to be fully explored. Motivated by several real applications, the investigator plans to: 1) develop nonparametric classification procedures based on DD (Depth-vs-Depth) plots. These procedures are referred to as DD-classifiers, and they are to be compared with the so-called support vector machine procedures; 2) use the multivariate spacings derived from data depth to: (2a) construct tolerance envelopes for functional or time series data and (2b) develop a class of multivariate goodness-of-fit tests.Classification is is an important task in all scientific domains, such as identifying new species in archaeological investigations or distinguishing disease types in medical studies. Applying the notion of data depth, the investigator proposes to develop effective classification procedures, which can automatically yield the best separating power for classification purposes and compete well with the highly calibrated existing classification procedures. The classification outcomes can be easily visualized in a two-dimensional plot regardless of the dimension of the data. The investigator also introduces multivariate spacings for the analysis of multi-dimensional data. These multivariate spacings should have a wide range of utilities. In particular, the investigator applies these spacings to develop both tolerance envelopes for tracking multivariate data and a class of multivariate goodness-of-fit tests. She plans to apply the proposed tolerance envelope to the monitoring of aircraft landing patterns and to ensure landing safety. She also plans to apply the proposed classifications to disease identification. These applications are motivated by the investigator's ongoing collaborative research projects with the Federal Aviation Administration and the Department of Psychiatry of the Robert Wood Johnson Medical School. The proposed projects involve real databases and are ideally suited for engaging students and postdocs.
|Effective start/end date||9/1/10 → 8/31/12|
- National Science Foundation (National Science Foundation (NSF))