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Wild adaptive trimming for robust estimation and cluster analysis

Author

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  • Andrea Cerioli
  • Alessio Farcomeni
  • Marco Riani

Abstract

Trimming principles play an important role in robust statistics. However, their use for clustering typically requires some preliminary information about the contamination rate and the number of groups. We suggest a fresh approach to trimming that does not rely on this knowledge and that proves to be particularly suited for solving problems in robust cluster analysis. Our approach replaces the original K‐population (robust) estimation problem with K distinct one‐population steps, which take advantage of the good breakdown properties of trimmed estimators when the trimming level exceeds the usual bound of 0.5. In this setting, we prove that exact affine equivariance is lost on one hand but, on the other hand, an arbitrarily high breakdown point can be achieved by “anchoring” the robust estimator. We also support the use of adaptive trimming schemes, in order to infer the contamination rate from the data. A further bonus of our methodology is its ability to provide a reliable choice of the usually unknown number of groups.

Suggested Citation

  • Andrea Cerioli & Alessio Farcomeni & Marco Riani, 2019. "Wild adaptive trimming for robust estimation and cluster analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(1), pages 235-256, March.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:1:p:235-256
    DOI: 10.1111/sjos.12349
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    Cited by:

    1. Alessio Farcomeni & Antonio Punzo, 2020. "Robust model-based clustering with mild and gross outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 989-1007, December.
    2. Cappozzo, Andrea & Greselin, Francesca & Murphy, Thomas Brendan, 2021. "Robust variable selection for model-based learning in presence of adulteration," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    3. Riani, Marco & Atkinson, Anthony Curtis & Corbellini, Aldo & Farcomeni, Alessio & Laurini, Fabrizio, 2024. "Information Criteria for Outlier Detection Avoiding Arbitrary Significance Levels," Econometrics and Statistics, Elsevier, vol. 29(C), pages 189-205.
    4. Marco Riani & Anthony C. Atkinson & Andrea Cerioli & Aldo Corbellini, 2019. "Comments on: Data science, big data and statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 349-352, June.
    5. Reiko Aoki & Juan P. M. Bustamante & Gilberto A. Paula, 2022. "Local influence diagnostics with forward search in regression analysis," Statistical Papers, Springer, vol. 63(5), pages 1477-1497, October.
    6. Francesca Torti & Marco Riani & Gianluca Morelli, 2021. "Semiautomatic robust regression clustering of international trade data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 863-894, September.
    7. Brenton R. Clarke & Andrew Grose, 2023. "A further study comparing forward search multivariate outlier methods including ATLA with an application to clustering," Statistical Papers, Springer, vol. 64(2), pages 395-420, April.

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