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Original Articles

Local influence analysis for regression models with scale mixtures of skew-normal distributions

, &
Pages 343-368 | Received 13 Feb 2009, Accepted 05 Oct 2009, Published online: 08 Oct 2010

References

  • Andrews , D. F. and Mallows , C. L. 1974 . Scale mixtures of normal distributions . J. R. Stat. Soc. B , 36 : 99 – 102 .
  • Arellano-Valle , R. B. , Bolfarine , H. and Lachos , V. H. 2005 . Skew-normal linear mixed models . J. Data Sci. , 3 : 415 – 438 .
  • Arellano-Valle , R. B. and Genton , M. G. 2005 . On fundamental skew distributions . J. Multivariate Anal. , 96 : 93 – 116 .
  • Azzalini , A. 1985 . A class of distributions which includes the normal ones . Scand. J. Stat. , 12 : 171 – 178 .
  • Azzalini , A. and Capitanio , A. 1999 . Statistical applications of the multivariate skew normal distribution . J. R. Stat. Soc. B , 61 : 579 – 602 .
  • Azzalini , A. and Capitanio , A. 2003 . Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution . J. R. Stat. Soc. B , 65 : 367 – 389 .
  • Azzalini , A. and Dalla-Valle , A. 1996 . The multivariate skew-normal distribution . Biometrika , 83 : 715 – 726 .
  • Azzalini , A. and Genton , M. G. 2008 . Robust likelihood methods based on the skew-t and related distributions . Int. Stat. Rev. , 76 : 106 – 129 .
  • Berkane , M. , Kano , Y. and Bentler , P. M. 1994 . Pseudo maximum likelihood estimation in elliptical theory: Effects of misspecification . Comput. Stat. Data Anal. , 18 : 255 – 267 .
  • Branco , M. D. and Dey , D. K. 2001 . A general class of multivariate skew-elliptical distributions . J. Multivariate Anal. , 79 : 99 – 113 .
  • Brownlee , K. A. 1960 . Statiscal Theory and Methodology in Science and Engineering , New York : Wiley .
  • Cook , R. D. 1977 . Detection of influential observations in linear regression . Technometrics , 19 : 15 – 18 .
  • Cook , R. D. 1986 . Assessment of local influence (with discussion) . J. R. Stat. Soc. B , 48 : 133 – 169 .
  • Galea-Rojas , M. , Paula , G. A. and Cysneiros , F. J.A. 2005 . On diagnostics in symmetrical nonlinear models . Stat. Prob. Lett. , 73 : 459 – 467 .
  • Galea-Rojas , M. , Paula , G. A. and Uribe-Opazo , M. 2003 . On influence diagnostic in univariate elliptical linear regression models . Stat. Pap. , 44 : 23 – 45 .
  • Johnson , N. L. , Kotz , S. and Balakrishnan , N. 1994 . Continuous Univariate Distributions , Vol. 1 , New York : John Wiley .
  • Kim , H. M. 2008 . A note on scale mixtures of skew normal distribution . Stat. Prob. Lett. , 78 : 1694 – 1701 .
  • Lachos , V. H. , Bolfarine , H. , Arellano-Valle , R. B. and Montenegro , L. C. 2007 . Likelihood based inference for multivariate skew-normal regression models . Commun. Stat. Theory Methods , 36 : 1769 – 1786 .
  • V.H. Lachos, P. Ghosh and R.B. Arellano-Valle, Likelihood based inference for skew-normal/independent linear mixed models, preprint (2009), to appear in Statistica Sinica
  • Lange , K. L. , Little , J. A. and Taylor , M. G. 1989 . Robust Statistical modeling using the t distribution . J. Am. Stat. Assoc. , 84 : 881 – 896 .
  • Lange , K. L. and Sinsheimer , J. S. 1993 . Normal/independent distributions and their applications in robust regression . J. Comput. Graph. Stat. , 2 : 175 – 198 .
  • Lee , S. Y. , Lu , B. and Song , X. Y. 2006 . Assessing local influence for nonlinear structural equation models with ignorable missing data . Comput. Stat. Data Anal. , 50 : 1356 – 1377 .
  • Lee , S. Y. and Xu , L. 2004 . Influence analysis of nonlinear mixed-effects models . Comput. Stat. Data Anal. , 45 : 321 – 341 .
  • Lessaffre , E. and Verbeke , G. 1998 . Local influence in linear mixed models . Biometrics , 54 : 570 – 582 .
  • Lin , T. I. , Lee , J. C. and Hsieh , W. J. 2007 . Robust mixture modeling using the skew t distribution . Stat. and Comput. , 17 : 81 – 92 .
  • Liu , C. 1996 . Bayesian roboust linear regression with incomplete data . J. Am. Stat. Assoc. , 91 : 1219 – 1227 .
  • Magnus , J. R. and Neudecker , H. 1988 . Matrix Differential Calculus with Applications in Statistics and Econometrics , New York : John Wiley .
  • Ortega , E. M. , Bolfarine , H. and Paula , G. A. 2003 . Influence diagnostics in generalized log-gamma regression models . Comput. Stat. Data Anal. , 42 : 165 – 186 .
  • Osorio , F. 2006 . “ Diagnóstico de influência em modelos elípticos com efeitos mistos ” . Brazil : Department of Statistics, University of São Paulo . Unpublished Ph.D. diss.
  • Osorio , F. , Paula , G. A. and Galea , M. 2007 . Assessment of local influence in elliptical linear models with longitudinal structure . Comput. Stat. Data Anal. , 51 : 4354 – 4368 .
  • Poon , W. Y. and Poon , Y. S. 1999 . Conformal normal curvature and assessment of local influence . J. R. Stat. Soc. B , 61 : 51 – 61 .
  • R Development Core Team, R: A Language and Environment for Stat. Computing, R Foundation for Stat. Computing, Vienna, Austria, ISBN 3-900051-07-0
  • M.C. Russo, G.A. Paula, and R. Aoki, Influence diagnosis in nonlinear mixed-effects elliptical models, preprint (2009), to appear in Computational Statistics & Data Analysis
  • Sahu , S. K. , Dey , D. K. and Branco , M. D. 2003 . A new class of multivariate skew distributions with applications to bayesian regression models . Can. J. Stat. , 31 : 129 – 150 .
  • Wang , J. , Boyer , J. and Genton , M. G. 2004 . A skew-symmetric representation of multivariate distributions . Stat. Sin. , 14 : 1259 – 1270 .
  • Wang , J. and Genton , M. G. 2006 . The multivariate skew-slash distribution . J. Stat. Plan. Inference , 136 : 209 – 220 .
  • Wei , G. C.G. and Tanner , M. A. 1990 . A monte carlo implementation of the EM algorithm and the poor man's data augmentation algorithms . J. Am. Stat. Assoc. , 85 : 699 – 704 .
  • Zhou , T. and He , X. 2008 . Three-step estimation in linear mixed models with skew-t distributions . J. Stat. Plan. Inference , 138 : 1542 – 1555 .
  • Zhu , H. and Lee , S. 2001 . Local influence for incomplete-data models . J. R. Stat. Soc. B , 63 : 111 – 126 .

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