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Utilizing the Flexibility of the Epsilon-Skew-Normal Distribution for Common Regression Problems

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  • Alan Hutson

Abstract

In this paper we illustrate the properties of the epsilon-skew-normal (ESN) distribution with respect to developing more flexible regression models. The ESN model is a simple one-parameter extension of the standard normal model. The additional parameter ~ corresponds to the degree of skewness in the model. In the fitting process we take advantage of relatively new powerful routines that are now available in standard software packages such as SAS. It is illustrated that even if the true underlying error distribution is exactly normal there is no practical loss n power with respect to testing for non-zero regression coefficients. If the true underlying error distribution is slightly skewed, the ESN model is superior in terms of statistical power for tests about the regression coefficient. This model has good asymptotic properties for samples of size n>50.

Suggested Citation

  • Alan Hutson, 2004. "Utilizing the Flexibility of the Epsilon-Skew-Normal Distribution for Common Regression Problems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(6), pages 673-683.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:6:p:673-683
    DOI: 10.1080/1478881042000214659
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    Cited by:

    1. Bondon, Pascal, 2009. "Estimation of autoregressive models with epsilon-skew-normal innovations," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1761-1776, September.
    2. Liqun Wang & Alexandre Leblanc, 2008. "Second-order nonlinear least squares estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 883-900, December.
    3. Alan D. Hutson & Gregory E. Wilding & Terry L. Mashtare & Albert Vexler, 2015. "Measures of biomarker dependence using a copula-based multivariate epsilon-skew-normal family of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2734-2753, December.
    4. Alan D. Hutson & Albert Vexler, 2018. "A Cautionary Note on Beta Families of Distributions and the Aliases Within," The American Statistician, Taylor & Francis Journals, vol. 72(2), pages 121-129, April.

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