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Robust estimation in the normal mixture model based on robust clustering

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  • J. A. Cuesta‐Albertos
  • C. Matrán
  • A. Mayo‐Iscar

Abstract

Summary. We introduce a robust estimation procedure that is based on the choice of a representative trimmed subsample through an initial robust clustering procedure, and subsequent improvements based on maximum likelihood. To obtain the initial trimming we resort to the trimmed k‐means, a simple procedure designed for finding the core of the clusters under appropriate configurations. By handling the trimmed data as censored, maximum likelihood estimation provides in each step the location and shape of the next trimming. Data‐driven restrictions on the parameters, requiring that every distribution in the mixture must be sufficiently represented in the initial clustered region, allow singularities to be avoided and guarantee the existence of the estimator. Our analysis includes robustness properties and asymptotic results as well as worked examples.

Suggested Citation

  • J. A. Cuesta‐Albertos & C. Matrán & A. Mayo‐Iscar, 2008. "Robust estimation in the normal mixture model based on robust clustering," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 779-802, September.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:4:p:779-802
    DOI: 10.1111/j.1467-9868.2008.00657.x
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    References listed on IDEAS

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    1. Marianthi Markatou, 2000. "Mixture Models, Robustness, and the Weighted Likelihood Methodology," Biometrics, The International Biometric Society, vol. 56(2), pages 483-486, June.
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    Cited by:

    1. Neykov, N.M. & Filzmoser, P. & Neytchev, P.N., 2012. "Robust joint modeling of mean and dispersion through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 34-48, January.
    2. L. A. García-Escudero & A. Gordaliza & C. Matrán & A. Mayo-Iscar, 2018. "Comments on “The power of monitoring: how to make the most of a contaminated multivariate sample”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 605-608, December.
    3. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.
    4. Gao, Jinxin & Hitchcock, David B., 2010. "James-Stein shrinkage to improve k-means cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2113-2127, September.
    5. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation In Extreme Value Regression Models Of Hedge Fund Tail Risks," Working Papers hal-04090916, HAL.
    6. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation in Extreme Value Regression Models of Hedge Fund Tail Risks," Papers 2304.06950, arXiv.org.
    7. Luis García-Escudero & Alfonso Gordaliza & Carlos Matrán & Agustín Mayo-Iscar, 2010. "A review of robust clustering methods," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(2), pages 89-109, September.

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