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A Generalized Additive Model for Binary Rare Events Data: An Application to Credit Defaults

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Analysis and Modeling of Complex Data in Behavioral and Social Sciences

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Abstract

We aim at proposing a new model for binary rare events, i.e. binary dependent variable with a very small number of ones. We extend the Generalized Extreme Value (GEV) regression model proposed by Calabrese and Osmetti (Journal of Applied Statistics 40(6):1172–1188, 2013) to a Generalized Additive Model (GAM). We suggest to consider the quantile function of the GEV distribution as a link function in a GAM, so we propose the Generalized Extreme Value Additive (GEVA) model. In order to estimate the GEVA model, a modified version of the local scoring algorithm of GAM is proposed. Finally, to model default probability, we apply our proposal to empirical data on Italian Small and Medium Enterprises (SMEs). The results show that the GEVA model has a higher predictive accuracy to identify the rare event than the logistic additive model.

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References

  • Agresti, A. (2002). Categorical data analysis. New York: Wiley.

    Book  MATH  Google Scholar 

  • Altman, E., & Sabato, G. (2006). Modeling credit risk for SMEs: evidence from the US market. Abacus, 19(6), 716–723.

    Google Scholar 

  • Ansell, J., Lin, S., Ma, Y., & Andreeva, G. (2009, August). Experimenting with modeling default of small and medium sized enterprises (SMEs). In Credit Scoring and Credit Control XI Conference.

    Google Scholar 

  • Basel Committee on Banking Supervision. (2005). International convergence of capital measurement and capital standards: A revised framework. Basel: Bank for International Settlements.

    Google Scholar 

  • Calabrese, R., & Osmetti, S. A. (2013). Modelling small and medium enterprise loan defaults as rare events: the generalized extreme value regression model. Journal of Applied Statistics, 40(6), 1172–1188.

    Article  Google Scholar 

  • Cerved Group. (2011, February). Caratteristiche delle imprese, governance e probabilità di insolvenza. Report. Milan.

    Google Scholar 

  • Ciampi, F., & Gordini, N. (2008). Using economic-financial ratios for small enterprize default prediction modeling: an empirical analysis. In Oxford Business & Economics Conference, Oxford.

    Google Scholar 

  • Falk, M., Haler, J., & Reiss, R. (2010). Laws of small numbers: extremes and rare events (3rd ed.). Basel: Springer.

    Google Scholar 

  • Fantazzini, D., & Figini, S. (2009). Random survival forests models for SME credit risk measurement. Methodology and Computing in Applied Probability, 11, 29–45.

    Article  MathSciNet  Google Scholar 

  • Fantazzini, D., Figini, S., De Giuli, E., & Giudici P. (2009). Enhanced credit default models for heterogeneous SME segments. Journal of Financial Transformation, 25(N.1), 31–39.

    Google Scholar 

  • Giudici, P. (2003). Applied data mining: statistical methods for business and industry. London: Wiley.

    Google Scholar 

  • Hand, D. J. (2009). Measuring classifier performance: a coherent alternative to the area under the ROC curve. Machine Learning, 77, 103–123.

    Article  Google Scholar 

  • Hastie, T. J., & Tibshirami, R. J. (1990). Generalized additive models. Boca Raton: Chapman & Hall.

    MATH  Google Scholar 

  • King, G., & Zeng, L. (2001). Logistic regression in rare events data. Political Analysis, 9, 321–354.

    Article  Google Scholar 

  • Kotz, S., & Nadarajah, S. (2000). Extreme value distributions. Theory and applications. London: Imperial Colleg Press.

    Book  MATH  Google Scholar 

  • Thomas, L., Edelman, D., & Crook, J. C. (2002). Credit scoring and its applications. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  MATH  Google Scholar 

  • Vozzella, P., & Gabbi, G. (2010). Default and asset correlation: An empirical study for Italian SMEs. Working Paper.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Essex Business School, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, UK

    Raffaella Calabrese

  2. Università Cattolica del Sacro Cuore di Milano, Largo Gemelli 1, 20123, Milano, Italy

    Silvia Angela Osmetti

Authors
  1. Raffaella Calabrese
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  2. Silvia Angela Osmetti
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Corresponding author

Correspondence to Silvia Angela Osmetti .

Editor information

Editors and Affiliations

  1. Department of Statistical Science, University of Rome "La Sapienza", Rome, Italy

    Donatella Vicari

  2. and Information Sciences, Tama University Graduate School of Management, Tokyo, Japan

    Akinori Okada

  3. Department of Political Science, University of Naples "Federico II", Naples, Italy

    Giancarlo Ragozini

  4. Fakultät Statistik, Technische Universität Dortmund, Dortmund, Germany

    Claus Weihs

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Calabrese, R., Osmetti, S.A. (2014). A Generalized Additive Model for Binary Rare Events Data: An Application to Credit Defaults. In: Vicari, D., Okada, A., Ragozini, G., Weihs, C. (eds) Analysis and Modeling of Complex Data in Behavioral and Social Sciences. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-06692-9_9

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