IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v31y2022i2d10.1007_s10260-021-00578-2.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-021-00578-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-021-00578-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Sugasawa, Shonosuke & Kobayashi, Genya, 2022. "Robust fitting of mixture models using weighted complete estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    4. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    5. Roberto Rocci & Stefano Antonio Gattone & Roberto Di Mari, 2018. "A data driven equivariant approach to constrained Gaussian mixture modeling," 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. 12(2), pages 235-260, June.
    6. Claudiu Vinte & Marcel Ausloos, 2022. "The Cross-Sectional Intrinsic Entropy. A Comprehensive Stock Market Volatility Estimator," Papers 2205.00104, arXiv.org.
    7. Nicodemo, Catia & Satorra, Albert, 2020. "Exploratory Data Analysis on Large Data Sets: The Example of Salary Variation in Spanish Social Security Data," IZA Discussion Papers 13459, Institute of Labor Economics (IZA).
    8. Oh, Man-Suk, 2014. "Bayesian comparison of models with inequality and equality constraints," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 176-182.
    9. Warshaw, Evan, 2020. "Asymmetric volatility spillover between European equity and foreign exchange markets: Evidence from the frequency domain," International Review of Economics & Finance, Elsevier, vol. 68(C), pages 1-14.
    10. Vincenzo Verardi, 2013. "Semiparametric regression in Stata," United Kingdom Stata Users' Group Meetings 2013 14, Stata Users Group.
    11. Mazo, Gildas & Averyanov, Yaroslav, 2019. "Constraining kernel estimators in semiparametric copula mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 170-189.
    12. Finger, Robert, 2012. "Biases in Farm-Level Yield Risk Analysis due to Data Aggregation," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 61(01), pages 1-14, February.
    13. Roberto Mari & Roberto Rocci & Stefano Antonio Gattone, 2020. "Scale-constrained approaches for maximum likelihood estimation and model selection of clusterwise linear regression models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 49-78, March.
    14. Hung Tong & Cristina Tortora, 2022. "Model-based clustering and outlier detection with missing data," 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. 16(1), pages 5-30, March.
    15. Shirin Enshaeifar & Ahmed Zoha & Andreas Markides & Severin Skillman & Sahr Thomas Acton & Tarek Elsaleh & Masoud Hassanpour & Alireza Ahrabian & Mark Kenny & Stuart Klein & Helen Rostill & Ramin Nilf, 2018. "Health management and pattern analysis of daily living activities of people with dementia using in-home sensors and machine learning techniques," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-20, May.
    16. Mario A. Rojas & Yuri A. Iriarte, 2022. "A Lindley-Type Distribution for Modeling High-Kurtosis Data," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    17. Maciej Kostrzewski & Jadwiga Kostrzewska, 2021. "The Impact of Forecasting Jumps on Forecasting Electricity Prices," Energies, MDPI, vol. 14(2), pages 1-17, January.
    18. 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.
    19. Salvatore Ingrassia & Simona Minotti & Giorgio Vittadini, 2012. "Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 363-401, October.
    20. Václav Plevka & Pieter Segaert & Chris M. J. Tampère & Mia Hubert, 2016. "Analysis of travel activity determinants using robust statistics," Transportation, Springer, vol. 43(6), pages 979-996, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stmapp:v:31:y:2022:i:2:d:10.1007_s10260-021-00578-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.