Sparse Functional Boxplots for Multivariate Curves

Abstract

This article introduces the sparse functional boxplot and the intensity sparse functional boxplot as practical exploratory tools. Besides being available for complete functional data, they can be used in sparse univariate and multivariate functional data. The sparse functional boxplot, based on the functional boxplot, displays sparseness proportions within the 50% central region. The intensity sparse functional boxplot indicates the relative intensity of fitted sparse point patterns in the central region. The two-stage functional boxplot, which derives from the functional boxplot to detect outliers, is furthermore extended to its sparse form. We also contribute to sparse data fitting improvement and sparse multivariate functional data depth. In a simulation study, we evaluate the goodness of data fitting, several depth proposals for sparse multivariate functional data, and compare the results of outlier detection between the sparse functional boxplot and its two-stage version. The practical applications of the sparse functional boxplot and intensity sparse functional boxplot are illustrated with two public health datasets. Supplementary materials and codes are available for readers to apply our visualization tools and replicate the analysis.

Keywords:

• Depth
• Missing values
• Multivariate functional data
• Outlier detection
• Sparse functional data
• Visualization

Supplementary Materials

Supplements: R-code for sparse and intensity functional boxplots: R-code for the commands sparse_fbplot and intensity_sparse_fbplot described in the articles (sparse_fbplot.R & intensity_sparse_fbplot.R). Simulation code: Simulation code for the optimal depth under eight models described in the article (00_execute_simulation_spearman.R) and the outlier detection under eight models described in the article (execute_outldetect.R). CD4 data: CD4 count for 366 subjects from 18 months before to 42 months after seroconversion, load cd4 (Goldsmith, Greven, and Crainiceanu 2013) in refund package. Malnutrition data: The original sparse prevalence of stunted growth and low birth height from 1985 to 2019 (malnutrition.csv). Supplementary Material: The performances of several depths and outlier detection under eight models in different sparseness types. All files can be found in a single zip file (sparse_fbplot.zip).

Additional information

Funding

This research was supported by the King Abdullah University of Science and Technology (KAUST).