Extensions of Stein's Lemma for the skew-normal distribution

Communications in Statistics - Theory and Methods

Volumn 36, Issue 9, 2007, Pages 1661-1671

  Adcock, C J ^a,b  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Hidden truncation models; Multivariate skew normal distribution; Portfolio selection; Siegel's formula; Stein's lemma; Utility functions

Indexed keywords

COVARIANCE MATRIX; FUNCTIONS; MATHEMATICAL MODELS; VECTORS;

HIDDEN TRUNCATION MODELS; MULTIVARIATE SKEW-NORMAL DISTRIBUTION; PORTFOLIO SELECTION; SIEGEL'S FORMULA; STEIN'S LEMMA; UTILITY FUNCTIONS;

STATISTICS;

EID: 34547253275     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920601126084     Document Type: Article

References (26)

1. Adcock, C. J., Shutes, K. (2001). Portfolio selection based on the multivariate skew-normal distribution. In: Skulimowski, A., ed. Financial Modelling. Krakow: Progress & Business Publishers, pp. 167-177.
2. Arnold, B. C., Beaver, R. J. (2000). Hidden truncation models. Sankhyā A 62:23-25.
3. Arnold, B. C., Beaver, R. J. (2004). Elliptical models subject to hidden truncation or selective sampling. In: Genton, M., ed. Skew Elliptical Distributions and Their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman and Hall/CRC, pp. 101-112.
4. Arrellano-Valle, R. B., Azzalini, A. (2004). On the unification of skew normal distributions. Scand. J. Statist. 14:561-574.
5. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12:171-178.
6. Azzalini, A. (1986). Further results on a class of distributions which includes the normal ones. Statistica 46:199-208.
7. Azzalini, A., Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83:715-726.
8. Del Helguero, F. (1908). Sulla rappresentazione analitica delle statistiche abnormali. Atti Del IV Congresso Internationale dei Matimatici 111:288-299.
9. Fama, E. (1970). Efficient capital markets: a review of theory and empirical work. J. Fin. 25:383-417.
10. González-Farías, G., Domínguez-Molina, A., Gupta, A. K. (2004). Additive properties of skew normal random vectors. J. Statist. Plann. Infer. 126:521-534.
11. O'Hagan, A., Leonard, T. (1976). Bayes estimation subject to uncertainty about parameter constraints. Biometrika 63:201-203.
12. Harvey, C. R., Leichty, J. C., Leichty, M. W., Muller, P. (2004). Portfolio selection with higher moments. In progress.
13. Horrace, W. C. (2005). Some results on the multivariate truncated normal distribution. J. Multivariate Anal. 94:209-221.
14. Kallberg, J. G., Ziemba, W. T. (1983). Comparison of alternative functions in portfolio selection problems. Manage. Sci. 11: 1257-1276.
15. Liu, J. S. (1994). Siegel's formula via Stein's identities. Statist. Probab. Lett. 21:247-251.
16. Markowitz, H. M. (1952). Portfolio selection. J. Fin. 7:77-91.
17. Markowitz, H. M. (1987). Mean Variance Analysis in Portfolio Choice and Capital Markets. Oxford: Blackwell.
18. Pratt, J. W. (1964). Risk aversion in the small and in the large. Econometrica 32:122-136.
19. Roberts, C. (1966). A correlation model useful in the study of twins. J. Amer. Statist. Assoc. 61:1184-1190.
20. Rubinstein, M. E. (1973). The fundamental theorem of parameter-preference security valuation. J. Financial Quantitative Anal. 8:61-70.
21. Shutes, K. (2005). Non-Normality in Asset Pricing - Extensions and Applications of the Skew-Normal Distribution. Ph.D. thesis, University of Sheffield, Sheffield, UK.
22. Siegel, A. F. (1993). A surprising covariance involving the minimum of multivariate normal variables. J. Amer. Statist. Assoc. 88:77-80.
23. Simaan, Y. (1993). Portfolio selection and asset pricing - three parameter framework. Manage. Sci. 39:568-587.
24. Stein, C. M. (1973). Estimation of the mean of a multivariate normal distribution. Proc. Prague Symp. Asymptotic Statist. 345-381.
25. Stein, C. M. (1981). Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9:1135-1151.
26. Tallis, G. M. (1961). The moment generating function of the truncated multi-normal distribution. J. Roy. Statist. Soc. B 23:223-229.