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Abstract

The variable selection is a challenging task in statistical analysis. In many real situations, a large number of potential predictors are available and a selection among them is recommended. For dealing with this problem, the automated procedures are the most commonly used methods, without taking into account their drawbacks and disadvantages. To overcome them, the shrinkage methods are a good alternative. Our aim is to investigate the performance of some variable selection methods, focusing on a statistical procedure suitable for the competing risks model. In this theoretical setting, the same variables might have different degrees of influence on the risks due to multiple causes and this has to be taken into account in the choice of the “best” subset. The proposed procedure, based on shrinkage techniques, is evaluated by means of empirical analysis on a data-set of financial indicators computed from a sample of industrial firms annual reports.

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Notes

  1. 1.

    In order to estimate the tuning parameter λ, the leave-one-out cross-validation is used [24, 37].

References

  1. Akaike, H.: Information Theory and an Extension of the Maximum Likelihood Principle. In: Petrov, B.N., Csaki F. (eds.) Second International Symposium on Information Theory, pp. 267–281 (1973)

    Google Scholar 

  2. Allison, P.D.: Discrete-time Methods for the Analysis of Event Histories. In: Leinhardt S. (eds.) Sociological Methodology, pp. 61–98. Jossey-Bass, San Francisco (1982)

    Google Scholar 

  3. Altaian, E.I.: Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy. J. of Finance 23, 589–609 (1968)

    Article  Google Scholar 

  4. Altaian, E.I.: Predicting financial distress of companies: revisiting the Z-score and ZTM model. New York University. Working Paper (2000)

    Google Scholar 

  5. Altman, E.I., Hochkiss, E.: Corporate Financial Distress and Bankruptcy: Predict and Avoid Bankruptcy, Analyze and Invest in Distressed Debt. John Wiley & Sons, New York (2006)

    Google Scholar 

  6. Amendola, A., Restaino, M., Sensini, L.: Variable selection in default risk model. J. of Risk Model Valid. 5(1), 3–19 (2011)

    Google Scholar 

  7. Antoniadis, A., Fryzlewicz, P., Letué, F.: The Dantzig selector in Cox’s proportional hazards model. Scand. J. of Stat. 37(4), 531–552 (2010)

    Article  MATH  Google Scholar 

  8. Andersen, P.K., Abildstrøm, S.Z., Rosthøj, S.: Competing Risks as a Multi-State Model, Stat. Methods in Med. Res. 11, 203–215 (2002)

    Article  MATH  Google Scholar 

  9. Andersen, P.K., Borgan, Ø., Gill, R.D., Keiding, N.: Statistical Models based on Counting Processes. Springer, Berlin (1993)

    Google Scholar 

  10. Brabazon, A., Keenan, P.B.: A Hybrid Genetic Model for the Prediction of Corporate Failure. Comput. Manag. Sci. 1(3–4), 293–310 (2004)

    MATH  Google Scholar 

  11. Breiman, L.: Heuristics of instability and stabilization in model selection. Ann. of Stat. 24(6), 2350–2383 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Chancharat, N., Tian, G., Davy, P., McCrae, M., Lodh, S.: Multiple States of Financially Distressed Companies: Tests using a Competing-Risks Model. Australas. Account. Bus. and Finance J. 4(4), 27–44 (2010)

    Google Scholar 

  13. Cox, D.R.: Partial likelihood. Biom. 62(2), 269–276 (1975)

    MATH  Google Scholar 

  14. Dakovic, R., Czado C, Berg D.: Bankruptcy prediction in Norway: a comparison study. Appl. Econ. Lett. 17, 1739–1746 (2010)

    Article  Google Scholar 

  15. Dimitras, A., Zanakis, S., Zopudinis, C.: A survey of businesses failures with an emphasis on failure prediction methods and industrial applications. Eur. J. of Oper. Res. 27, 337–357 (1996)

    Google Scholar 

  16. Dyrberg, A.: Firms in Financial Distress: An Exploratory Analysis. Working Paper 17/2004, Financial Market, Danmarks Nationalbank and Centre for Applied Microeconometrics (CAM), Institute of Economics, University of Copenhagen (2004)

    Google Scholar 

  17. Efron, B., Hastie, T., Johnstone, T., Tibshirani, R.: Least angle regression. Ann. of Stat. 32, 407–499 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Engelmann, B., Hayden, E., Tasche, D.: Testing rating accuracy. Risk 16, 82–86 (2003)

    Google Scholar 

  19. Fan, J., Li, R.: Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties. J. of the Am. Stat. Assoc. 96(456), 1348–1360 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  20. Fan, J., Li, R.: Variable selection for Cox’s proportional hazards model and frailty model. Ann. of Stat. 30, 74–99 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  21. Fan, J., Lv, J.: Selective overview of variable selection in high dimensional feature space. Stat. Sinica 20, 101–148 (2010)

    MATH  MathSciNet  Google Scholar 

  22. Faraggi, D., Simon, R.: Bayesian variable selection method for censored survival data. Biom. 54(4), 1475–1485 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  23. Frank, I.E., Friedman, J.H.: A Statistical View of Some Chemometrics Regression Tools. Technometrics 35, 109–148 (1993)

    Article  MATH  Google Scholar 

  24. Friedman, J., Hastie, T., Tibshirani, R.: Regularization Paths for Generalized Linear Models via Coordinate Descent. J. of Stat. Softw. 33(1), 1–22 (2010)

    Google Scholar 

  25. Hougaard, P.: Analysis of Multivariate Survival Data, Statistics for Biology and Health. Springer, New York (2000)

    Google Scholar 

  26. Hunter, D.R., Li, R.: Variable selection using MM algorithm. Ann. of Stat. 44(5), 1617–1642 (2005)

    Article  MathSciNet  Google Scholar 

  27. Ibrahim, J.G., Chen, M.-H., McEachern, S.N.: Bayesian Variable Selection for Proportional Hazards Models. Can. J. of Stat. 27, 701–717 (1999)

    Article  MATH  Google Scholar 

  28. Johnsen, T., Melicher, R.W.: Predicting corporate bankruptcy and financial distress: Information value added by multinomial logit models. J. of Econ. and Bus. 46(4), 269–286 (1994)

    Article  Google Scholar 

  29. Jones, S., Hensher, D.A.: Modelling corporate failure: a multinomial nested logit analysis for unordered outcomes. The Brit. Acc. Rev. 39, 89–107 (2007)

    Article  Google Scholar 

  30. Perederiy, V.: Bankruptcy Prediction Revisited: Non-Traditional Ratios and Lasso Selection. (Available at SSRN, 2009) http://ssrn.com/abstract=1518084 or http://dx.doi.org/ 10.2139/ssrn.l518084

    Google Scholar 

  31. Prantl, S.: Bankruptcy and voluntary liquidation: Evidence for new firms in East and West Germany after unification. Discussion paper no.03–72, ZEW, Centre for European Economic Research, London, pp. 1–42 (2003)

    Google Scholar 

  32. Rommer, A.D.: Firms in financial distress: an exploratory analysis. Working paper no.17, Danmarks Nationalbank and Centre for Applied Microeconometrics (CAM), Institute of Economics, University of Copenhagen, Copenhagen, pp. 1–68 (2004)

    Google Scholar 

  33. Sauerbrei, W., Schumacher, M.: A bootstrap resampling procedure for model building: application to the Cox regression model. Stat. in Med. 11(16), 2093–2109 (1992)

    Article  Google Scholar 

  34. Schary, M.: The probability of exit. RAND J. of Econ. 22, 339–353 (1991)

    Article  Google Scholar 

  35. Schwarz, G.: Estimating the Dimension of a Model. Ann. of Stat. 6(2), 461–464 (1978)

    Article  MATH  Google Scholar 

  36. Shumway, T.: Forecasting bankruptcy more accurately: A simple hazard model. J. of Bus. 74(1), 101–124 (2001)

    Article  MathSciNet  Google Scholar 

  37. Simon, N., Friedman, J., Hastie, T., Tibshirani, R.: Regularization Paths for Cox’s Proportional Hazards Model via Coordinate Descent. J. of Stat. Softw. 39(5), 1–13 (2011)

    Google Scholar 

  38. Tibshirani, R.: Regression Shrinkage and Selection via the Lasso. J. of R. Stat. Soc. Ser. B 58, 267–288 (1996)

    MathSciNet  Google Scholar 

  39. Tibshirani, R.: The lasso method for variable selection in the Cox model. Stat. in Med. 16, 385–395 (1997)

    Google Scholar 

  40. Zou, H., Hastie, T.: Regularization and Variable Selection via the Elastic Net. J. of the R. Stat. Soc. Ser. B 67(Part 2), 301–320 (2005)

    Article  MathSciNet  Google Scholar 

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Correspondence to Marialuisa Restaino .

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Amendola, A., Restaino, M., Sensini, L. (2014). An Empirical Comparison of Variable Selection Methods in Competing Risks Model. In: Corazza, M., Pizzi, C. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-02499-8_2

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