Discussion of “Multivariate functional outlier detection”
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This interesting paper adds on the authors long and outstanding trajectory in robust statistics and , more specifically, on robust functional data analysis. We congratulate Mia Hubert, Peter Rousseeuw and Pieter Segaert for this important contribution.
As the authors point out, most of the literature to date on functional outlier detection deals with univariate functional data (one curve observed by individual). This work considers the case of p-variate functional data (p curves observed by individual). The paper discusses carefully the problem of outlier detection in this setting and starts by establishing a classification of different outlying behaviours. Then, several p-variate functional depths and distance functions are defined by integrating over time the existing or newly defined p-variate counterparts. Finally, by combining these measures, several graphical diagnostic tools are proposed.
We would like to contribute to the discussion by focusing on two aspects....
KeywordsOutlier Detection Functional Data Analysis Detection Rule Shape Outlier Functional Depth
We would like to acknowledge Mia Hubert, Peter Rousseeuw and Pieter Segaert for kindly providing all the data sets and the R code of all the procedures described in their article.
- Hubert M, Rousseeuw PJ, Segaert P (2015) Multivariate functional outlier detection. Stat Methods Appl. doi: 10.1007/s10260-015-0297-8