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A best linear threshold classification with scale mixture of skew normal populations

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  • Hea-Jung Kim

Abstract

This paper describes a threshold classification with $$K$$ K populations whose membership category is associated with the threshold process of a latent variable. It is seen that the optimal procedure (Bayes procedure) for the classification involves a nonlinear classification rule and hence, its analytic properties and an efficient estimation can not be explored due to its complex distribution. As an alternative, this paper proposes the best linear procedure and verifies its effectiveness. For this, the present paper provides the necessary theories for deriving the linear rule and its properties, an efficient inference, and a simulation study that sheds light on the performance of the best linear procedure. It also provides three real data examples to demonstrate the applicability of the best linear procedure. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Hea-Jung Kim, 2015. "A best linear threshold classification with scale mixture of skew normal populations," Computational Statistics, Springer, vol. 30(1), pages 1-28, March.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:1:p:1-28
    DOI: 10.1007/s00180-014-0517-y
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    References listed on IDEAS

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    1. José R. Berrendero & Javier Cárcamo, 2012. "The Tangent Classifier," The American Statistician, Taylor & Francis Journals, vol. 66(3), pages 185-194, August.
    2. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
    3. ., 1999. "The assessment of capital adequacy," Chapters, in: Handbook of Banking Regulation and Supervision in the United Kingdom, chapter 17, Edward Elgar Publishing.
    4. Srivastava, M. S., 1984. "A measure of skewness and kurtosis and a graphical method for assessing multivariate normality," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 263-267, October.
    5. Tzy-Chy Lin & Tsung-I Lin, 2010. "Supervised learning of multivariate skew normal mixture models with missing information," Computational Statistics, Springer, vol. 25(2), pages 183-201, June.
    6. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    7. Kim, Hea-Jung, 2008. "A class of weighted multivariate normal distributions and its properties," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1758-1771, September.
    8. Lounasheimo, Antton, 1999. "The Impact of Human Capital on Economic Growth," Discussion Papers 673, The Research Institute of the Finnish Economy.
    9. Lin, Tsung I. & Ho, Hsiu J. & Chen, Chiang L., 2009. "Analysis of multivariate skew normal models with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2337-2351, November.
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