2011/01/01 by Ying Sun, Marc G. Genton · 1 citation
Mathematics · Economics, Econometrics and Finance · #Advanced Statistical Methods and Models #Statistical Methods and Inference #Financial Risk and Volatility Modeling
paper · doi:10.1198/jcgs.2011.09224
openalex publication_date 2011/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
This article proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outward 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. The construction of a functional boxplot is illustrated on a series of sea surface temperatures related to the El Niño 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, respectively. This article has supplementary material online.