A Matrix Variate Closed Skew-Normal Distribution with Applications to Stochastic Frontier Analysis

References

• Aigner , D. , Lovell , C. A. K. , Schmidt , P. ( 1977 ). Formulation and estimation of stochastic frontier production function models . J. Econometrics 6 : 21 – 37 .
   Google Scholar
• Azzalini , A. ( 2005 ). The skew-normal distribution and related multivariate families . Scand. J. Statist. 32 : 159 – 188 .
   Web of Science ®Google Scholar
• Azzalini , A. , Capitanio , A. ( 1999 ). Statistical applications of the multivariate skew-normal distributions . J. Roy. Statist. Soc. B 61 : 579 – 602 .
   Google Scholar
• Coelli , T. J. , Prasada Rao , D. S. , O'Donnell , C. J. , Battese , G. ( 2005 ). An Introduction to Efficiency and Productivity Analysis . New York : Springer Science+Business Media .
   Google Scholar
• Copas , J. B. , Li , H. G. ( 1997 ). Inference for non-random samples . J. Roy. Statist. Soc. B 59 : 55 – 95 .
   Google Scholar
• Domínguez-Molina , J. A. , González-Farías , G. , Gupta , A. K. ( 2003 ). The multivariate closed skew normal distribution . Technical Report No. 03-12 , Department of Mathematics and Statistics, Bowling Green State University , Bowling Green , OH .
   Google Scholar
• Domínguez-Molina , J. A. , González-Farías , G. , Ramos-Quiroga , R. ( 2004 ). Skew normality in stochastic frontier analysis . In: Genton , M. G. , ed. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality . Boca Raton , FL : Chapman and Hall/CRC , pp. 223 – 241 .
   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. , He , L. , Liu , X. ( 2001 ). Moments of skew-normal random vectors and their quadratic forms . Statist. Probab. Lett. 51 : 319 – 325 .
   Web of Science ®Google Scholar
• González-Farías , G. , Domínguez-Molina , J. A. , Gupta , A. K. ( 2004a ). The closed skew-normal distribution . In: Genton M. G. , ed. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality . Boca Raton , FL : Chapman and Hall/CRC , pp. 25 – 42 .
   Google Scholar
• González-Farías , G. , Domínguez-Molina , J. A. , Gupta , A. K. ( 2004b ). Additive properties of skew normal random vectors . J. Statist. Plann. Infer. 126 : 521 – 534 .
   Web of Science ®Google Scholar
• Gupta , A. K. , Nagar , D. K. ( 2000 ). Matrix Variate Distributions . Boca Raton , FL : Chapman & Hall/CRC .
   Google Scholar
• Horn , R. A. , Johnson , C. R. ( 1985 ). Matrix Analysis . Cambridge : Cambridge University Press .
   Google Scholar
• Loperfido , N. ( 2001 ). Quadratic forms of skew-normal random vectors . Statist. Probab. Lett. 54 : 381 – 387 .
   Web of Science ®Google Scholar
• Meeusen , W. , van Den Broeck , J. ( 1977 ). Efficiency estimation from Cobb-Douglas production functions with composed error . Int. Economic Rev. 18 : 435 – 444 .
   Web of Science ®Google Scholar
• Nelsen , R. B. ( 2006 ). An Introduction to Copulas. , 2nd ed. New York : Springer Science+Business Media .
   Google Scholar
• Pewsey , A. ( 2000 ). Problems of inference for Azzalini's skew-normal distribution . J. Appl. Statist. 27 : 859 – 870 .
   Web of Science ®Google Scholar
• Rao , C. R. ( 1973 ). Linear Statistical Inference and its Applications. , 2nd ed. New York : Wiley .
   Google Scholar
• Wang , J. , Boyer , J. , Genton , M. G. ( 2004 ). A note on the equivalence between chi-square and generalized skew-normal distributions . Statist. Probab. Lett. 66 : 395 – 398 .
   Web of Science ®Google Scholar