A class of rectangle-screened multivariate normal distributions and its applications

References

• Genton MG. Skew-elliptical distributions and their applications; A journey beyond normality. New York: Chapman & Hall; 2004.
   Google Scholar
• Marchenko YV, Genton MG. A Heckman selection-t model. Journal of the American Statistical Association. 2012;107:304–317. doi: 10.1080/01621459.2012.656011
   Web of Science ®Google Scholar
• Rubin DB. Inference and missing data. Biometrika. 1976;63:581–592.
   Google Scholar
• Azzalini A. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics. 1985;12:171–178.
   Web of Science ®Google Scholar
• Rao CR. Weighted distributions arising out of methods of ascertainment. In: Aitkinson AG, Feinberg SE, editors. A Celebration of Statistics: The ISI Centenary Volume. New York: Springer; 1985.
   Google Scholar
• Arnold BC, Beaver RJ, Groeneveld RA, Meeker WQ. The nontruncated marginal of a truncated bivariate normal distribution. Psychometrica. 1993;58:471–478. doi: 10.1007/BF02294652
   Web of Science ®Google Scholar
• Arellano-Valle RB, Branco MD, Genton MG. A unified view on skewed distributions arising from selections. The Canadian Journal of Statistics. 2006;34:581–601. doi: 10.1002/cjs.5550340403
   Web of Science ®Google Scholar
• Azzalini A, Dalla Valle A. The multivariate skew-normal distribution. Biometrika. 1996;83:715–726. doi: 10.1093/biomet/83.4.715
   Web of Science ®Google Scholar
• Arellano-Valle RB, Azzalini A. On unification of families of skew-normal distributions. Scandinavian Journal of Statistics. 2006;33:561–574. doi: 10.1111/j.1467-9469.2006.00503.x
   Web of Science ®Google Scholar
• Branco MD, Dey DK. A general class of multivariate skew-normal distributions. Journal of Multivariate Analysis. 2001;79:99–113. doi: 10.1006/jmva.2000.1960
   Web of Science ®Google Scholar
• Ma Y, Genton MG, Tsiatis AA. Locally efficient semiparametric estimators for generalized skew-elliptical distributions. Journal of the American Statistical Association. 2005;100:980–989. doi: 10.1198/016214505000000079
   Web of Science ®Google Scholar
• Kim HJ. A class of weighted multivariate normal distributions and its properties. Journal of Multivariate Analysis. 2008;99:1758–1771. doi: 10.1016/j.jmva.2008.01.008
   Web of Science ®Google Scholar
• Arnold BC, Beaver RJ. Skewed multivariate models related to hidden truncation and/or selective reporting. Test. 2002;11:7–54.
   Google Scholar
• Genton MG. Discussion of ‘The skew-normal’. Scandinavian Journal of Statistics. 2005;32:189–198.
   Google Scholar
• Genz A, Bretz F, Miwa T, Mi X, Leish F, Scheipl F, Bornkamp B, Hothorn T. mvtnorm: Multivariate normal and t distributions, URL http://cran.r-project.org/web/packages/mvtnorm/index.html, R package version 0.9-9992; 2012.
   Google Scholar
• Joe H. Approximation to multivariate rectangle probabilities based on conditional expectations. Journal of the American Statistical Association. 1995;90:957–966. doi: 10.1080/01621459.1995.10476596
   Web of Science ®Google Scholar
• Azzalini A, Capitanio A. Statistical applications of the multivariate skew-normal distribution. Journal of the Royal Statistical Society, Series B. 1999;61:579–602. doi: 10.1111/1467-9868.00194
   Google Scholar
• Devroye L. Non-uniform random variate generation. New York: Springer Verlag; 1986.
   Google Scholar
• Horrace WC. Some results on the multivariate truncated normal distribution. Journal of Multivariate Analysis. 2005;94:209–221. doi: 10.1016/j.jmva.2004.10.007
   Web of Science ®Google Scholar
• Box GE, Tiao GC. Bayesian inference in statistical analysis. Reading, MA: Addison-Wesley; 1973.
   Google Scholar
• Basilevsky A. Applied matrix algebra in the statistical sciences. New York: Dover; 1983.
   Google Scholar
• Manjunath BG, Wilhelm S. Moments calculation for the double truncated multivariate normal density. Working Paper; 2009. Available at SSRN: http://ssrn.com/abstract=1472153.
   Google Scholar
• Kotz S, Balakrishnan N, Johnson NL. Continuous multivariate distributions Vol. 1. 2nd ed. New York: Wiley; 2000.
   Google Scholar
• Meng X, Rubin DB. Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika. 1993;80:267–278. doi: 10.1093/biomet/80.2.267
   Web of Science ®Google Scholar
• Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B. 1977;39:1–38.
   Google Scholar
• Kim H-M, Kim HJ. Multivariate screened normal classification analysis. Konkuk University, Technical report; 2013.
   Google Scholar
• Boys RJ, Dunsmore IR. Screening in a normal model. Journal of the Royal Statistical Society, Series B. 1986;48:60–69.
   Google Scholar
• Rencher AC, Schaalje GB. Linear models in statistics. 2nd ed. New York: Wiley; 2008.
   Google Scholar
• Judge GG, Yancey TA, Bock ME, Bohrer R. The non-optimality of the inequality restricted estimator under squared error loss. Journal of Econometrics 1984;25:165–177. doi: 10.1016/0304-4076(84)90044-7
   Web of Science ®Google Scholar
• Gourieroux C, Holly A, Monfort A. Likelihood ratio test, Wald test, and Kuhn-Yucker test in linear models with inequality constraints on the regression parameters. Econometrica. 1982;50:63–80.
   Google Scholar
• Geweke J. Exact inference in the inequality constrained normal linear regression model. Journal of Applied Econometrics. 1986;1:127–141. doi: 10.1002/jae.3950010203
   Google Scholar
• Davis WW. Bayesian analysis of the linear model subject to linear inequality constraints. Journal of the American Statistical Association. 1978;73:573–579. doi: 10.1080/01621459.1978.10480057
   Web of Science ®Google Scholar
• Press SJ. Applied multivariate analysis: Using Bayesian and frequentist methods of inference. Florida: Krieger; 1982.
   Google Scholar
• Odell PL, Feiveson AH. A numerical procedure to generate a sample covariance matrix. Journal of the American Statistical Association. 1996;61:199–203. doi: 10.1080/01621459.1966.10502018
   Google Scholar
• Srivastava MS. Methods of multivariate statistics. New York: Wiley; 2002.
   Google Scholar