Modeling skew-symmetric distributions using B-spline and penalties

Journal of Statistical Planning and Inference

Volumn 141, Issue 8, 2011, Pages 2878-2890

  Frederic, Patrizio ^a  

^a UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

Author keywords

B spline; Penalized likelihood; Skew symmetric distributions

Indexed keywords

EID: 79954620588     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2011.03.011     Document Type: Article

References (26)

1. Azzalini A. A class of distributions which includes the normal ones. Scand. J. Statist. 1985, 12(2):171-178.
2. Azzalini A. Further results on a class of distributions which includes the normal ones. Scand. J. Statist. 1986, 46:199-208.
3. Azzalini A. The skew-normal distribution and related multivariate families. Scand. J. Statist. 2005, 32(2):159-200. (with discussion by Marc G. Genton and a rejoinder by the author).
4. Azzalini A., Capitanio A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. J. Roy. Statist. Soc. Ser. B: Statist. Methodol. 2003, 65(2):367-389.
5. Azzalini A., Dalla Valle A. The multivariate skew-normal distribution. Biometrika 1996, 83:715-726.
6. Azzalini A., Genton M. Robust likelihood methods based on the skew-t and related distributions. Internat. Statist. Rev. 2008, 76(1):106-129.
7. Azzalini A., Genton M.G., Scarpa B. Invariance-based estimating equations for skew-symmetric distributions, Metron. Skew-symmetric and flexible distributions 2010, 68:353-377.
8. Branco M.D., Dey D.K. A general class of multivariate skew-elliptical distributions. J. Multivariate Anal. 2001, 79:99-113.
9. de Boor C. A practical guide to splines, revised edition. Applied Mathematical Sciences, vol. 27 2001, Springer-Verlag, New York.
10. Di Ciccio T., Monti A. Inferential aspects of the skew exponential power distribution. J. Amer. Statist. Assoc. 2004, 99(January):439-450.
11. Ditzian Z., Totik V. Moduli of smoothness. Springer Series in Computational Mathematics, vol. 9 1987, Springer-Verlag, New York.
12. Eilers P.H.C., Currie I.D., Durbán M. Fast and compact smoothing on large multidimensional grids. Comput. Statist. Data Anal. 2006, 50(1):61-76.
13. Eilers P.H.C., Marx B.D. Flexible smoothing with B-splines and penalties. Statist. Sci. 1996, 11(2):89-121.
14. Eilers, P.H.C., Marx, B.D., 2004. Splines, knots, and penalties, unpublished. URL http://www.stat.lsu.edu/faculty/marx/splines-knots-penalties.pdf.
15. Frederic P., Catellani M. Statistical analysis of an industrial distillation process. Statist. Appl. 2003, 15(2):263-273.
16. Genton M.G. Skew-symmetric and generalized skew-elliptical distributions. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality 2004, Chapman & Hall/CRC, Boca Raton, FL, pp. 81-100.
17. Genton M.G. Discussion of "the skew-normal". Scand. J. Statist. 2005, 32(2):189-198.
18. Genton M.G., Loperfido N.M.R. Generalized skew-elliptical distributions and their quadratic forms. Ann. Inst. Statist. Math. 2005, 57(2):389-401.
19. Loperfido N.M.R. Generalized skew-normal distributions. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality 2004, Chapman & Hall/CRC, Boca Raton, FL, pp. 65-80.
20. Ma Y., Genton M.G. Flexible class of skew-symmetric distributions. Scand. J. Statist. 2004, 31(3):459-468.
21. Ma Y., Genton M.G., Tsiatis A.A. Locally efficient semiparametric estimators for generalized skew-elliptical distributions. J. Amer. Statist. Assoc. 2005, 100(471):980-989.
22. Ma Y., Hart J.D. Constrained local likelihood estimators for semiparametric skew-normal distributions. Biometrika 2007, 94(1):119-134.
23. R Development Core Team, 2009. R: A language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria, ISBN 3-900051-07-0 http://www.R-project.org.
24. Subbotin Y. Spline approximation. Encyclopaedia of Mathematics, Supplement I 2002, Kluwer Academic Publishers, Dordrecht. M. Hazewinkel (Ed.).
25. Wahba G. Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. Roy. Statist. Soc. Ser. B Statist. Methodol. 1978, 40:362-364.
26. Wang J., Boyer J., Genton M.G. A skew-symmetric representation of multivariate distributions. Statist. Sinica 2004, 14(4):1259-1270.