A0643
Title: Test for outlier detection by high-dimensional PCA
Authors: Yugo Nakayama - Nissan Motor Co., Ltd. (Japan) [presenting]
Kazuyoshi Yata - University of Tsukuba (Japan)
Makoto Aoshima - University of Tsukuba (Japan)
Abstract: Outlier detection for high-dimensional, low sample size (HDLSS) data is studied. Theories and methodologies for high-dimensional data have become increasingly important in many fields. In particular, there has been a strong demand for HDLSS analysis. Principal component analysis (PCA) is investigated under the HDLSS settings. However, there are still some areas where analysis methods have not been fully established, one of which is outlier detection. For high-dimensional data, classical methods based on the Mahalanobis distance are usually not applicable, so an alternative is needed. One of the methods for the univariate data is the Smirnov-Grubbs test. We propose a new outlier detection by applying high-dimensional PC scores to the Smirnov-Grubbs test. By using the asymptotic properties of the PC scores, we evaluate its size and power. Our results show that the proposed method gives preferable performances in the HDLSS setting. Finally, we check the performance of the outlier detection method in both numerical and real data analysis.
