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Statistical analysis of variable-structure models

Author

Listed:
  • Aivazian, Sergey

    (CEMI RAS, Moscow; School of Economics, Moscow, Russia)

  • Bereznyatskiy, Alexander

    (Economics and Mathematics Institute (CEMI RAS), Moscow, Russian Federation)

  • Brodsky, Boris

    (Economics and Mathematics Institute (CEMI RAS), Moscow, Russian Federation)

  • Darkhovsky, Boris

    (Institute for Systems Analysis, Moscow, Russian Federation)

Abstract

Classification problems for univariate and multivariate observations are often encountered in statistics and economics. However, all existing approaches to solving these problems have several essential drawbacks: 1. All these methods cannot help in testing the null hypothesis of no different classes; 2. The number of classes is assumed to be known a priori; 3. Theoretical justification of performance effectiveness of these methods is lacking. In this paper a new nonparametric method is proposed which can help us to solve these problems. This method enables us to construct consistent estimate of an unknown number of classes and to test the null hypothesis of no different classes. Besides theoretical findings, we present results of experimental analysis of this method including comparison of its characteristics with the maximum likelihood method and k-means method in different situations.

Suggested Citation

  • Aivazian, Sergey & Bereznyatskiy, Alexander & Brodsky, Boris & Darkhovsky, Boris, 2015. "Statistical analysis of variable-structure models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 84-105.
    • Handle: RePEc:ris:apltrx:0273
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    References listed on IDEAS

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    More about this item

    Keywords

    nonparametric methods; cluster analysis; classification methods; EM algorithm; k-means; mixture models;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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