Stein’s Lemma for generalized skew-elliptical random vectors

References

• Adcock, C. J. 2007. Extensions of Stein’s lemma for the skew-normal distribution. Communications in Statistics - Theory and Methods 36 (9):1661–71. doi:10.1080/03610920601126084.
   Web of Science ®Google Scholar
• Adcock, C. J. 2010. Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution. Annals of Operations Research 176 (1):221–34. doi:10.1007/s10479-009-0586-4.
   Web of Science ®Google Scholar
• Adcock, C. J. 2014. Mean-variance-skewness efficient surfaces, Stein’s Lemma and the multivariate extended skew-student distribution. European Journal of Operational Research 234 (2):392–401. doi:10.1016/j.ejor.2013.07.011.
   Web of Science ®Google Scholar
• Adcock, C. J. 2018. The skew-normal and related distributions as a copula and as a model for skewness persistence. Paper Presented at the 2018 CFM Conference, Pisa.
   Google Scholar
• Arashi, M., and S. M. M. Tabatabaey. 2010. A note on classical Stein-type estimators in elliptically contoured models. Journal of Statistical Planning and Inference 140 (5):1206–13. doi:10.1016/j.jspi.2009.11.001.
   Web of Science ®Google Scholar
• Arellano-Valle, R. B., H. W. Gomez, and F. A. Quintana. 2004. A new class of skew-normal distributions. Communications in Statistics - Theory and Methods 33 (7):1465–80. doi:10.1081/STA-120037254.
   Web of Science ®Google Scholar
• Bodnar, T., and A. K. Gupta. 2015. Robustness of the inference procedures for the global minimum variance portfolio weights in a skew-normal model. The European Journal of Finance 21 (13–14):1176–94. doi:10.1080/1351847X.2012.696073.
   Web of Science ®Google Scholar
• Branco, M. D., and D. K. Dey. 2001. A general class of multivariate skew-elliptical distributions. Journal of Multivariate Analysis 79 (1):99–113. doi:10.1006/jmva.2000.1960.
   Web of Science ®Google Scholar
• Brown, L., A. DasGupta, L. R. Haff, and W. E. Strawderman. 2006. The heat equation and Stein’s identity: Connections, applications. Journal of Statistical Planning and Inference 136 (7):2254–78. doi:10.1016/j.jspi.2005.12.001.
   Web of Science ®Google Scholar
• Cambanis, S., S. Huang, and G. Simons. 1981. On the theory of elliptically contoured distributions. Journal of Multivariate Analysis 11 (3):368–85. doi:10.1016/0047-259X(81)90082-8.
   Web of Science ®Google Scholar
• DasGupta, A. 2007. Stein’s identity, fisher information, and projection pursuit: A triangulation. Journal of Statistical Planning and Inference 137 (11):3394–409. doi:10.1016/j.jspi.2007.03.019.
   Web of Science ®Google Scholar
• Eling, M. 2014. Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models? Insurance: Mathematics and Economics 59:45–56. doi:10.1016/j.insmatheco.2014.08.004.
   Web of Science ®Google Scholar
• Exton, H. 1976. Multiple hypergeometric functions and applications. Chichester: Ellis Horwood.
   Google Scholar
• Framstad, N. C. 2011. Portfolio separation properties of the skew-elliptical distributions, with generalizations. Statistics & Probability Letters 81:1862–6. doi:10.1016/j.spl.2011.07.006.
   Web of Science ®Google Scholar
• Genton, M. G. (Ed.). 2004. Skew-elliptical distributions and their applications: A journey beyond normality. Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Genton, M. G., and N. M. Loperfido. 2005. Generalized skew-elliptical distributions and their quadratic forms. Annals of the Institute of Statistical Mathematics 57 (2):389–401. doi:10.1007/BF02507031.
   Web of Science ®Google Scholar
• Huang, W.-J., N.-C. Su, and A. K. Gupta. 2013. A Study of generalized skew- normal distribution. Statistics 47 (5):942–53. doi:10.1080/02331888.2012.697164.
   Web of Science ®Google Scholar
• Landsman, Z. 2006. On the generalization of Stein’s Lemma for elliptical class of distributions. Statistics & Probability Letters 76:1012–6. doi:10.1016/j.spl.2005.11.004.
   Web of Science ®Google Scholar
• Landsman, Z., and E. A. Valdez. 2003. Tail conditional expectations for elliptical distributions. North American Actuarial Journal 7 (4):55–71. doi:10.1080/10920277.2003.10596118.
   Google Scholar
• Landsman, Z., and J. Nešlehova. 2008. Stein’s Lemma for elliptical random vectors. Journal of Multivariate Analysis 99 (5):912–27. doi:10.1016/j.jmva.2007.05.006.
   Web of Science ®Google Scholar
• Landsman, Z., S. Vanduffel, and J. Yao. 2013. A note on Stein’s lemma for multivariate elliptical distributions. Journal of Statistical Planning and Inference 143 (11):2016–22. doi:10.1016/j.jspi.2013.06.003.
   Web of Science ®Google Scholar
• Landsman, Z., U. Makov, and T. Shushi. 2013. Tail conditional expectations for generalized skew—elliptical distributions. Available at SSRN 2298265.
   Google Scholar
• Landsman, Z., U. Makov, and T. Shushi. 2017. Extended generalized skew-elliptical distributions and their moments. Sankhya A 79 (1):76–100. doi:10.1007/s13171-016-0090-2.
   Google Scholar
• Liu, J. S. 1994. Siegel’s formula via Stein’s identities. Statistics & Probability Letters 21 (3):247–51. doi:10.1016/0167-7152(94)90121-X.
   Web of Science ®Google Scholar
• Loperfido, N. 2014. Linear transformations to symmetry. Journal of Multivariate Analysis 129:186–92. doi:10.1016/j.jmva.2014.04.018.
   Web of Science ®Google Scholar
• Loperfido, N. 2018. Skewness-based projection pursuit: A computational approach. Computational Statistics & Data Analysis 120:42–57. doi:10.1016/j.csda.2017.11.001.
   Web of Science ®Google Scholar
• Nadarajah, S. 2009. The product t density distribution arising from the product of two Student’s t PDFs. Statistical Papers 50 (3):605–15. doi:10.1007/s00362-007-0088-x.
   Web of Science ®Google Scholar
• Shushi, T. 2016. A proof for the conjecture of characteristic function of the generalized skew-elliptical distributions. Statistics & Probability Letters 119:301–4. doi:10.1016/j.spl.2016.08.017.
   Web of Science ®Google Scholar
• Shushi, T. 2017. Skew-elliptical distributions with applications in risk theory. European Actuarial Journal 7 (1):277–20. doi:10.1007/s13385-016-0144-9.
   Web of Science ®Google Scholar
• Shushi, T. 2018. Generalized skew-elliptical distributions are closed under affine transformations. Statistics & Probability Letters 134:1–4. doi:10.1016/j.spl.2017.10.012.
   Web of Science ®Google Scholar
• Siegel, A. F. 1993. A Surprising Covariance Involving the Minimum of Multivariate Normal Variables. Journal of the American Statistical Association 88:77–80. doi:10.1080/01621459.1993.10594296.
   Web of Science ®Google Scholar
• Stein, C. M. 1981. Estimation of the mean of a multivariate normal distribution. The Annals of Statistics 9 (6):1135–51. doi:10.1214/aos/1176345632.
   Web of Science ®Google Scholar
• Vanduffel, S., and J. Yao. 2017. A stein type lemma for the multivariate generalized hyperbolic distribution. European Journal of Operational Research 261 (2):606–12. doi:10.1016/j.ejor.2017.03.008.
   Web of Science ®Google Scholar