Multivariate Linear Regression Model with Elliptically Contoured Distributed Errors and Monotone Missing Dependent Variables

References

• Anderson , T. W. ( 1957 ). Maximum likelihood estimates for multivariate normal distribution when some observations are missing . J. Amer. Statist. Assoc. 52 : 200 – 203 .
   Web of Science ®Google Scholar
• Anderson , T. W. , Fang , K. T. , Hsu , H. ( 1986 ). Maximum-likelihood estimators and likelihood-ratio criteria for multivariate elliptically contoured distributions . Canad. J. Statist. 14 : 55 – 59 .
   Web of Science ®Google Scholar
• Batsidis , A. , Zografos , K. ( 2005 ). Multivariate linear regression model with elliptically contoured distributed errors and monotone missing dependent variables . Technical Report No 14 (June 2005), Department of Mathematics, University of Ioannina, Greece .
   Google Scholar
• Batsidis , A. , Zografos , K. (2006). Statistical inference for location and scale of elliptically contoured models with monotone missing data. J. Statist. Plann. Infer. 136:2606–2629.
   Web of Science ®Google Scholar
• Blattberg , R. C. , Gonedes , N. J. ( 1974 ). A comparison of the stable and student distributions as statistical models for stock prices . J. Bus. 47 : 244 – 280 .
   Web of Science ®Google Scholar
• Chung , H. , Han , C. ( 2000 ). Discriminant analysis when a block of observations is missing . Ann. Ins. Statist. Math. 52 : 544 – 556 .
   Web of Science ®Google Scholar
• Cysneiros , F. J. A. , Paula , G. A. ( 2004 ). One-sided tests in linear models with multivariate t-distribution . Commun. Statist. Simul. Computat. 33 : 747 – 771 .
   Web of Science ®Google Scholar
• Cysneiros , F. J. A. , Paula , G. A. ( 2005 ). Restricted methods in symmetrical linear regression models . Computat. Statist. Data Anal. 49 : 689 – 708 .
   Web of Science ®Google Scholar
• Diaz-Garcia , J. A. , Rojas , M. G. , Leiva-Sanchez , V. ( 2003 ). Influence diagnostics for elliptical multivariate linear regression models . Commun. Statist. Theor. Meth. 32 : 625 – 642 .
   Web of Science ®Google Scholar
• Fama , E. F. ( 1965 ). The behaviour of stock market prices . J. Bus. 38 : 34 – 105 .
   Web of Science ®Google Scholar
• Fang , K. T. , Kotz , S. , Ng , K. W. ( 1990 ). Symmetric Multivariate and Related Distributions . London , New York : Chapman and Hall .
   Google Scholar
• Fang , K. T. , Zhang , Y. T. ( 1990 ). Generalized Multivariate Analysis . Berlin : Science Press , Beijing: Springer-Verlag .
   Google Scholar
• Fujisawa , H. ( 1995 ). A note on the maximum likelihood estimators for multivariate normal distribution with monotone data . Commun. Statist. Theor. Meth. 24 : 1377 – 1382 .
   Web of Science ®Google Scholar
• Galea , M. , Paula , G. A. , Bolfarine , H. ( 1997 ). Local influence in elliptical linear regression models . Statistician 46 : 71 – 79 .
   Google Scholar
• Gupta , A. K. , Varga , T. ( 1993 ). Elliptically Contoured Models in Statistics . Kluwer Academic Publishers .
   Google Scholar
• Gupta , A. K. , Nagar , D. K. ( 2000 ). Matrix Variate Distributions . London : Chapman and Hall .
   Google Scholar
• Hao , J. , Krishnamoorthy , K. ( 2001 ). Inferences on a normal covariance matrix and generalized variance with monotone missing data . J. Multivariate Anal. 78 : 62 – 82 .
   Web of Science ®Google Scholar
• Jinadasa , K. G. , Tracy , D. S. ( 1992 ). Maximum likelihood estimation for multivariate normal distribution with monotone sample . Commun. Statist. Theor. Meth. 21 : 41 – 50 .
   Web of Science ®Google Scholar
• Kanda , T. , Fujikoshi , Y. ( 1998 ). Some basic properties of the MLE'S for a multivariate normal distribution with monotone missing data . Amer. J. Mathemat. Manage. Sci. 18 : 161 – 190 .
   Google Scholar
• Kano , Y. ( 1994 ). Consistency property of elliptical probability density functions . J. Multivariate Anal. 51 : 139 – 147 .
   Web of Science ®Google Scholar
• Krishnamoorthy , K. , Pannala , M. K. ( 1998 ). Some simple test procedures for normal mean vector with incomplete data . Ann. Ins. Statist. Math. 50 : 531 – 542 .
   Web of Science ®Google Scholar
• Little , R. J. A. ( 1992 ). Regression with Missing X's: a review . J. Amer. Statist. Assoc. 87 : 1227 – 1237 .
   Web of Science ®Google Scholar
• Little , R. J. A. , Rubin , D. B. ( 2002 ). Statistical Analysis with Missing Data . New York : Wiley .
   Google Scholar
• Liu , C. ( 1996 ). Bayesian robust multivariate linear regression with incomplete data . J. Amer. Statist. Assoc. 91 : 1219 – 1227 .
   Web of Science ®Google Scholar
• Liu , S. ( 2002 ). Local influence in multivariate elliptical linear regression models . Lin. Algebra Applic. 354 : 159 – 174 .
   Web of Science ®Google Scholar
• Muirhead , R. J. ( 1982 ). Aspects of Multivariate Statistical Theory . New York : John Wiley and Sons .
   Google Scholar
• Raats , V. M. ( 2004 ). Approximations of the generalized Wilks' distribution . CentER Discussion Paper No.2004–85, Tilburg University. http://greywww.kub.nl:2080/greyfiles/center/2004/doc/85.pdf .
   Google Scholar
• Raats , V. M. , van der Genugten , B. B. , Moors , J. J. A. ( 2004 ). Asymptotics of multivariate regression with consecutively added variables . CentER Discussion Paper No. 2004-77, Tilburg University. http://greywww.kub.nl:2080/greyfiles/center/2004/doc/77.pdf .
   Google Scholar
• Raats , V. M. , van der Genugten , B. B. , Moors , J. J. A. (2005). Multivariate regression with consecutively added dependent variables. Lin. Algebra Applic. 410:170–197.
   Web of Science ®Google Scholar
• Rao , C. R. ( 1973 ). Linear Statistical Inference and Its Applications . New York : John Wiley and Sons .
   Google Scholar
• Rao , C. R. , Toutenburg , H. ( 1999 ). Linear Models: Least Squares and Alternatives . Springer-Verlag .
   Google Scholar
• Robins , J. M. , Rotnitzky , A. ( 1995 ). Semiparametric efficiency in multivariate regression models with missing data . J. Amer. Statist. Assoc. 90 : 122 – 129 .
   Web of Science ®Google Scholar
• Rubin , D. B. ( 1976 ). Inference and missing data . Biometrika 63 : 581 – 592 .
   Web of Science ®Google Scholar
• Schafer , J. L. ( 1997 ). Analysis of Incomplete Multivariate Data . London : Chapman and Hall .
   Google Scholar
• Singh , R. S. ( 1988 ). Estimation of error variance in linear regression models with errors having multivariate student-t distribution with unknown degrees of freedom . Econ. Lett. 27 : 47 – 53 .
   Web of Science ®Google Scholar
• Siotani , M. , Hayakawa , T. , Fujikoshi , Y. ( 1985 ). Modern Multivariate Statistical Analysis: A Graduate Course and Handbook . American Sciences Press .
   Google Scholar
• Sutradhar , B. C. , Ali , M. M. ( 1986 ). Estimation of the parameters of a regression model with a multivariate t error variable . Commun. Statist. Theor. Meth. 15 : 429 – 450 .
   Web of Science ®Google Scholar
• Tang , G. , Little , R. J. A. , Raghunathan , T. E. ( 2003 ). Analysis of multivariate missing data with nonignorable nonresponse . Biometrika 90 : 747 – 764 .
   Web of Science ®Google Scholar
• Zellner , A. ( 1976 ). Bayesian and non-Bayesian analysis of the regression model with multivariate student-t error terms . J. Amer. Statist. Assoc. 71 : 400 – 405 .
   Web of Science ®Google Scholar