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Original Articles

Extending the Scope of Inverse Regression Methods in Sufficient Dimension Reduction

Pages 84-95 | Received 27 Nov 2008, Accepted 20 Sep 2009, Published online: 22 Sep 2010

References

  • Cook , R. D. ( 1994 ). On the interpretation of regression plots . J. Amer. Statist. Assoc. 89 : 177 – 189 .
  • Cook , R. D. ( 1996 ). Graphics for regression with a binary response . J. Amer. Statist. Assoc. 91 : 983 – 992 .
  • Cook , R. D. ( 1998 ). Regression Graphics: Ideas for Studying Regressions Through Graphics . New York : Wiley & Sons .
  • Cook , R. D. , Li , B. (2002). Dimension reduction for conditional mean in regression. Ann. Statist. 30:455–474.
  • Cook , R. D. , Nachtsheim , C. J. ( 1994 ). Re-weighting to achieve elliptically contoured covariates in regression . J. Amer. Statist. Assoc. 89 : 592 – 599 .
  • Cook , R. D. , Weisberg , S. ( 1991 ). Discussion to “Sliced inverse regression for dimension reduction” . J. Amer. Statist. Assoc. 86 : 316 – 342 .
  • Eaton , M. L. ( 1986 ). A characterization of spherical distributions . J. Multivariate Anal. 34 : 439 – 446 .
  • Ferré , L. ( 1998 ). Determing the dimension in sliced inverse regression and related methods . J. Amer. Statist. Assoc. 93 : 132 – 140 .
  • Hall , P. , Li , K. C. ( 1993 ). On almost linearity of low dimensional projection from high dimensional data . Ann. Statist. 21 : 867 – 889 .
  • Li , K. C. ( 1991 ). Sliced inverse regression for dimension reduction (with discussion) . J. Amer. Statist. Assoc. 86 : 316 – 342 .
  • Li , K. C. ( 1992 ). On principal Hessian directions for data visuallization and dimension reduction: Another application of Stein's lemma . J. Amer. Statist. Assoc. 87 : 1025 – 1039 .
  • Li , B. , Dong , Y. X. ( 2009 ). Dimension reduction for non-elliptically distributed predictors . Ann. Statist. 37 : 1272 – 1298 .
  • Li , K. C. , Duan , N. H. ( 1989 ). Regression analysis under link violation . Ann. Statist. 17 : 1009 – 1052 .
  • Li , B. , Wang , S. L. ( 2007 ). On directional regression for dimension reduction . J. Amer. Statist. Assoc. 102 : 997 – 1008 .
  • Li , Y. X. , Zhu , L. X. ( 2007 ). Asymptotics for sliced average variance estimation Ann. Statist. 35 : 41 – 69 .
  • Li , L. , Cook , R. D. , Nachtsheim , C. J. ( 2005 ). Model-free variable selection . J. Roy. Statist. Soc. Ser. B 67 : 285 – 299 .
  • Li , B. , Zha , H. , Chiaromonte , F. ( 2005 ). Contour regression: A general approach to dimension reduction . Ann. Statist. 33 : 1580 – 1616 .
  • Zhou , J. H. , He , X. M. ( 2008 ). Dimension reduction based on constrained canonical correlation and variable filtering . Ann. Statist. 36 : 1649 – 1668 .
  • Zhu , L. X. , Ng , K. W. ( 1995 ). Asymptotics of sliced inverse regression . Statist. Sinica 5 : 727 – 736 .
  • Zhu , L. P. , Yu , Z. ( 2007 ). On spline approximation of sliced inverse regression . Sci. China Ser. A: Math. 50 : 1289 – 1302 .
  • Zhu , L. P. , Zhu , L. X. ( 2010 ). Dimension reduction in regressions via average partial mean estimation . J. Amer. Statist. Assoc. (In press) .
  • Zhu , L. P. , Zhu , L. X. , Ferré , L. , Wang , T. ( 2010 ). Sufficient dimension reduction through discretization-expectation estimation . Biometrika 97 : 295 – 304 .

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