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Estimation and computations for Gaussian mixtures with uniform noise under separation constraints

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  • Pietro Coretto

    (University of Salerno)

Abstract

In this paper we study a finite Gaussian mixture model with an additional uniform component that has the role to catch points in the tails of the data distribution. An adaptive constraint enforces a certain level of separation between the Gaussian mixture components and the uniform component representing noise and outliers in the tail of the distribution. The latter makes the proposed tool particularly useful for robust estimation and outlier identification. A constrained ML estimator is introduced for which existence and consistency is shown. One of the attractive features of the methodology is that the noise level is estimated from data. We also develop an EM-type algorithm with proven convergence. Based on numerical evidence we show how the methods developed in this paper are useful for several fundamental data analysis tasks: outlier identification, robust location-scale estimation, clustering, and density estimation.

Suggested Citation

  • Pietro Coretto, 2022. "Estimation and computations for Gaussian mixtures with uniform noise under separation constraints," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 427-458, June.
    • Handle: RePEc:spr:stmapp:v:31:y:2022:i:2:d:10.1007_s10260-021-00578-2
    DOI: 10.1007/s10260-021-00578-2
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    References listed on IDEAS

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    1. Pietro Coretto & Christian Hennig, 2010. "A simulation study to compare robust clustering methods based on mixtures," 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 111-135, September.
    2. R. M. Kuiper & H. Hoijtink & M. J. Silvapulle, 2011. "An Akaike-type information criterion for model selection under inequality constraints," Biometrika, Biometrika Trust, vol. 98(2), pages 495-501.
    3. Pietro Coretto & Christian Hennig, 2016. "Robust Improper Maximum Likelihood: Tuning, Computation, and a Comparison With Other Methods for Robust Gaussian Clustering," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1648-1659, October.
    4. Pietro Coretto & Michele La Rocca & Giuseppe Storti, 2020. "Improving Many Volatility Forecasts Using Cross-Sectional Volatility Clusters," JRFM, MDPI, vol. 13(4), pages 1-23, March.
    5. Salvatore Ingrassia, 2004. "A likelihood-based constrained algorithm for multivariate normal mixture models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(2), pages 151-166, September.
    6. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
    7. 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.
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