Nonlinear regression using order statistics from the multivariate generalized hyperbolic distributions

Abstract In this paper, by considering an -dimensional random vector from the multivariate generalized hyperbolic (GH) distribution, we derive the joint distribution of Y and the order statistics from We show that this joint distribution is indeed a mixture of the selection GH distributions. The results were applied to some regression functions via the order statistics and established with a real data set.

[1]  W. Breymann,et al.  ghyp: A package on generalized hyperbolic distributions , 2009 .

[2]  Christine M. Anderson-Cook,et al.  Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp. , 2017, Extremes.

[3]  R. Arellano-Valle,et al.  On the Unification of Families of Skew‐normal Distributions , 2006 .

[4]  N. Balakrishnan,et al.  Distribution of linear combinations of unordered and ordered components of an elliptical random vector , 2012 .

[5]  N. Loperfido,et al.  The exact sampling distribution of L-statistics , 2003 .

[6]  M. Viana.  Order Statistics - Handbook of Statistics, Vol. 16, Chapter 19, 1998. LINEAR COMBINATIONS OF ORDERED SYMMETRIC OBSERVATIONS WITH APPLICATIONS TO VISUAL ACUITY , 1998 .

[7]  K. Prause.  The Generalized Hyperbolic Model: Estimation, Financial Derivatives, and Risk Measures , 1999 .

[8]  A. Jamalizadeh,et al.  Regression analysis using order statistics , 2011 .

[9]  O. Barndorff-Nielsen.  Exponentially decreasing distributions for the logarithm of particle size , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[10]  Ingram Olkin,et al.  Correlation Analysis of Extreme Observations from a Multivariate Normal Distribution , 1995 .

[11]  Rostislav S. Protassov,et al.  EM-based maximum likelihood parameter estimation for multivariate generalized hyperbolic distributions with fixed λ , 2004, Stat. Comput..

[12]  E. Eberlein,et al.  Hyperbolic distributions in finance , 1995 .

[13]  Ole E. Barndorff-Nielsen,et al.  Hyperbolic Distributions and Ramifications: Contributions to Theory and Application , 1981 .

[14]  M. Viana.  19 Linear combinations of ordered symmetric observations with applications to visual acuity , 1998 .

[15]  Marek Arendarczyk,et al.  The joint distribution of the sum and maximum of dependent Pareto risks , 2018, J. Multivar. Anal..

[16]  Yi-Ping Chang,et al.  Testing Symmetry of a NIG Distribution , 2005 .

[17]  N. Loperfido.  Modeling maxima of longitudinal contralateral observations , 2008 .

[18]  Narayanaswamy Balakrishnan,et al.  Prediction in a trivariate normal distribution via a linear combination of order statistics , 2009 .

[19]  N. Balakrishnan,et al.  Prediction based on linear combinations of order statistics and bivariate concomitants in the case of multivariate elliptical distributions , 2014 .

[20]  Order statistics and their concomitants from multivariate normal mean–variance mixture distributions with application to Swiss Markets Data , 2017 .

[21]  M. Genton,et al.  A unified view on skewed distributions arising from selections , 2006 .