Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Hidden Truncation Normal Regression

  • Kim, Sungsu (Applied Statistics Unit, Indian Statistical Institute)
  • Received : 2012.08.29
  • Accepted : 2012.10.12
  • Published : 2012.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we propose regression methods based on the likelihood function. We assume Arnold-Beaver Skew Normal(ABSN) errors in a simple linear regression model. It was shown that the novel method performs better with an asymmetric data set compared to the usual regression model with the Gaussian errors. The utility of a novel method is demonstrated through simulation and real data sets.

Keywords

References

  1. Arnold, B. C. and Beaver, R. (2000). Hidden truncation models, Sankhya: The Indian Journal of Statistics, 62, 23-35.
  2. Azzalini, A. (1986). A class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171-178.
  3. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew normal distribution, Biometrika, 83, 715-726. https://doi.org/10.1093/biomet/83.4.715
  4. Bianco, A., Ben, M. and Yohai, V. (2005). Robust estimation for linear regression with asymmetric errors, Canadian Journal of Statistics, 33, 511-528. https://doi.org/10.1002/cjs.5550330404
  5. Cook, R. D. and Weisberg, S. (1994). An Introduction to Regression Graphics, John Wiley and Sons, Inc., New York.
  6. Kim, S. (2009). Inverse Circular Regression with Possibly Asymmetric Error Distribution, PhD Dissertation, University of California, Riverside.
  7. Kutner, M. H. (2004). Applied Linear Regression Models, 4th ed., New York.
  8. Marazzi, A. and Yohai, V. (2002). Adaptive truncated maximum likelihood regression with asymmetric errors, Journal of Statistical Planning and Inference, 122, 271-291.
  9. SenGupta, A. and Ugwuowo, F. (2006). Asymmetric circular-linear multivariate regression models with applications to environmental data, Environmental and Ecological Statistics, 13, 299-309. https://doi.org/10.1007/s10651-005-0013-1