Functional Boxplots for Complex Data Visualization

• Activity Number: 2
• Type: Invited
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Marc G. Genton*+ and Ying Sun
• Companies: Texas A & M University and Texas A & M University
• Keywords: depth ; functional ; precipitation ; space-time ; visualization

Abstract

We propose an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outwards ordering induced by band depth for functional data, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve and the maximum non-outlying envelope. In addition, outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the rule for classical boxplots. We further propose a method to correct the factor 1.5 in order to account for possible correlations in spatio-temporal data. The construction of a functional boxplot is illustrated on a series of sea surface temperatures related to the El Nino phenomenon and its outlier detection performance is explored by simulations. As applications, the functional boxplot and enhanced functional boxplot are demonstrated on children growth data and spatio-temporal U.S. precipitation data for nine climatic regions.