Robust Functional Principal Components Analysis for Skewed Distributions and Its Application to Outlier Detection

• Activity Number: 576
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: SSC
• Author(s): Liangliang Wang*+ and Nancy Heckman and Matias Salibián-Barrera
• Companies: The University of British Columbia and The University of British Columbia and The University of British Columbia
• Keywords: Robust functional PCA ; skewed distributions ; outlier detection ; medcouple

Abstract

Our work is motivated by an outlier detection problem for the radiosonde data in which the basic data structure is functional data: temperature as a function of pressure. The primary statistical problem is to determine objective ways of detecting unusual observations. To detect atypical observations we use the standardized difference between observed and fitted curves, obtained with functional PCA through conditional expectation (PACE). Unfortunately PACE is not robust and the estimates from it are significantly affected by outliers. We use a straightforward idea to robustify PACE by obtaining robust estimates of the mean and covariance functions. Estimating these functions robustly is challenging because skewness and outliers are present at the same time.