Functional boxplots based on epigraphs and hypographs

Abstract

Functional boxplot is an attractive technique to visualize data that come from functions. We propose an alternative to the functional boxplot based on depth measures. Our proposal generalizes the usual construction of the box-plot in one dimension related to the down-upward orderings of the data by considering two intuitive pre-orders in the functional context. These orderings are based on the epigraphs and hypographs of the data that allow a new definition of functional quartiles which is more robust to shape outliers. Simulated and real examples show that this proposal provides a convenient visualization technique with a great potential for analyzing functional data and illustrate its usefulness to detect outliers that other procedures do not detect.

Keywords:

• functional data
• box and whisker plot
• functional quartiles
• functional data orderings
• data visualization

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The authors would like to thank research projects MTM2012-36163-C06-03, ECO2011-25706 and ECO2012-38442 (Ministerio de Economía y Competitividad, Spain), FQM-329 and P11-FQM-7603 (Junta de Andalucía, Spain), all with EU ERD Funds.

Notes

1. More specifically, the data are in the zip file datasets under the name of the article Functional Boxplots. The files called sfitreg1cy.data and similar contain the curves for different regions.