Functional Boxplots for Complex Data Visualization

• Activity Number: 400
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Ying Sun*+ and Marc Genton
• Companies: Texas A&M University and Texas A&M University
• Keywords: Depth ; Functional data ; Growth data ; Precipitation data ; Space-time data

Abstract

This paper proposes an informative exploratory tool, the functional boxplot, for visualizing complex datasets, as well as its generalization, the enhanced functional boxplot. Based on the center outwards ordering induced by band depth for functional data, the five descriptive statistics of a functional boxplot are: the upper and lower boundaries of the central 50% region, the median, the minimum and the maximum boundaries. In addition, outliers can be detected in a functional boxplot by a proposed empirical rule analog to the 1.5 times the inter-quartile range rule for classical boxplots. 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, respectively.