Functional outlier detection and taxonomy by sequential transformations

Embargo End Date
2022-04-18

Type
Article

Authors
Dai, Wenlin
Mrkvička, Tomáš
Sun, Ying
Genton, Marc G.

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Environmental Statistics Group
Spatio-Temporal Statistics and Data Analysis Group
Statistics Program

Preprint Posting Date
2018-08-16

Online Publication Date
2020-04-03

Print Publication Date
2020-09

Date
2020-04-03

Submitted Date
2019-06-30

Abstract
Functional data analysis can be seriously impaired by abnormal observations, which can be classified as either magnitude or shape outliers based on their way of deviating from the bulk of data. Identifying magnitude outliers is relatively easy, while detecting shape outliers is much more challenging. We propose turning the shape outliers into magnitude outliers through data transformation and detecting them using the functional boxplot. Besides easing the detection procedure, applying several transformations sequentially provides a reasonable taxonomy for the flagged outliers. A joint functional ranking, which consists of several transformations, is also defined here. Simulation studies are carried out to evaluate the performance of the proposed method using different functional depth notions. Interesting results are obtained in several practical applications.

Citation
Dai, W., Mrkvička, T., Sun, Y., & Genton, M. G. (2020). Functional outlier detection and taxonomy by sequential transformations. Computational Statistics & Data Analysis, 149, 106960. doi:10.1016/j.csda.2020.106960

Acknowledgements
This research was supported by the King Abdullah University of Science and Technology (KAUST). Wenlin Dai is also supported by the National Natural Science Foundation of China (Grant No. 11901573).

Publisher
Elsevier BV

Journal
Computational Statistics & Data Analysis

DOI
10.1016/j.csda.2020.106960

arXiv
1808.05414

Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S0167947320300517

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