Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Further Applications of Johnson's SU-normal Distribution to Various Regression Models

  • Choi, Pilsun (Department of International Trade, Konkuk University) ;
  • Min, In-Sik (Department of Economics, Kyung Hee University)
  • Published : 2008.03.30
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Abstract

This study discusses Johnson's $S_U$-normal distribution capturing a wide range of non-normality in various regression models. We provide the likelihood inference using Johnson's $S_U$-normal distribution, and propose a likelihood ratio (LR) test for normality. We also apply the $S_U$-normal distribution to the binary and censored regression models. Monte Carlo simulations are used to show that the LR test using the $S_U$-normal distribution can be served as a model specification test for normal error distribution, and that the $S_U$-normal maximum likelihood (ML) estimators tend to yield more reliable marginal effect estimates in the binary and censored model when the error distributions are non-normal.

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References

  1. Andrews, D. W. K. (1997). A conditional Kolmogorov test. Econometrica, 65, 1097-1128 https://doi.org/10.2307/2171880
  2. Bollerslev, T. (1987). A conditionally heteroskedastic time series model for speculative prices and rates of return. The Review of Economics and Statistics, 69, 542-547 https://doi.org/10.2307/1925546
  3. Choi, P. (2002). Essays on modeling asymmetric and leptokurtic distributions of asset returns, Ph.D. Thesis, Texas A&M University
  4. Choi, P. and Min, I. (2007). Estimating endogenous switching regression model with a °exible parametric distribution function: application to Korean housing demand. Forthcoming in Applied Economics
  5. Choi, P. and Nam, K. (2007). Asymmetric and leptokurtic distribution for heteroscedas- tic asset returns: the $S_U-normal$ distribution. Forthcoming in Journal of Empirical Finance
  6. Fan, Y., Li, Q. and Min, I. (2006). A nonparametric bootstrap test of conditional distributions. Econometric Theory, 22, 587-613
  7. Hansen, B. E. (1994). Autoregressive conditional density estimation. International Economic Review, 35, 705-730 https://doi.org/10.2307/2527081
  8. Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika, 36, 149-176 https://doi.org/10.1093/biomet/36.1-2.149
  9. Klaauw, B. and Konig, R. H. (2003). Testing the normality assumption in the sample selection model with an application to travel demand. Journal of Business and Economic Statistics, 21, 31-42 https://doi.org/10.1198/073500102288618739
  10. van der Klaauw, B. and Konig, R. H. (2003). Testing the normality assumption in the sample selection model with an application to travel demand. Journal of Business and Economic Statistics, 21, 31-42 https://doi.org/10.1198/073500102288618739
  11. McDonald, J. B. (1996). An application and comparison of some flexible parametric and semi-parametric qualitative response models. Economics Letters, 53, 145-152 https://doi.org/10.1016/S0165-1765(96)00907-X
  12. McDonald, J. B. and Yexiao, J. X. (1996). A comparison of semi-parametric and partially adaptive estimators of the censored regression model with possibly skewed and leptokurtic error distributions. Economics Letters, 53, 153-159 https://doi.org/10.1016/S0165-1765(96)00906-8
  13. Rockinger, M. and Jondeau, E. (2001). Entropy Densities with an application to autore- gressive conditional skewness and kurtosis. Journal of Econometrics, 106, 119-142
  14. Theodossiou, P. (1998). Financial data and the skewed generalized T distribution. Management Science, 44, 1650-1661 https://doi.org/10.1287/mnsc.44.12.1650
  15. Theodossiou, P. (2000). Distribution of financial asset prices, the skewed generalized error distribution, and the pricing of options. Working Paper, Rutgers University
  16. Zheng, J. X. (2000). A consistent test of conditional parametric distributions. Econometric Theory, 16, 667-691 https://doi.org/10.1017/S026646660016503X

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