Dimension Reduction in Regressions through Weighted Variance Estimation

References

• Box , G. E. P. , Draper , N. ( 1987 ). Empirical Model-Building and Response Surface . New York : Wiley .
   Google Scholar
• Carroll , R. J. , Fan , J. , Gijbels , I. , Wand , M. P. (1997). Generalized partially linear single-index models. J. Amer. Statist. Assoc. 92:477–489.
   Web of Science ®Google Scholar
• Cook , R. D. ( 1998 ). Regression Graphics: Ideas for Studying Regressions Through Graphics . New York : Wiley & Sons .
   Google Scholar
• Cook , R. D. , Critchley , F. ( 2000 ). Identifying regression outliers and mixtures graphically . J. Amer. Statist. Assoc. 95 : 781 – 794 .
   Web of Science ®Google Scholar
• Cook , R. D. , Li , B. ( 2002 ). Dimension reduction for conditional mean in regression . Ann. Statist. 30 : 455 – 474 .
   Web of Science ®Google Scholar
• Cook , R. D. , Ni , L. ( 2005 ). Sufficient dimension reduction via inverse regression: a minimum discrepancy approach . J. Amer. Statist. Assoc. 100 : 410 – 428 .
   Web of Science ®Google Scholar
• Cook , R. D. , Weisberg , S. ( 1991 ). Discussion to “Sliced inverse regression for dimension reduction.” J. Amer. Statist. Assoc. 86 : 316 – 342 .
   Web of Science ®Google Scholar
• Diaconis , P. , Freedman , D. ( 1984 ). Asymptotics of graphical projection pursuit . Ann. Statist. 12 : 793 – 815 .
   Web of Science ®Google Scholar
• Fan , J. Q. , Peng , H. ( 2004 ). Nonconcave penalized likelihood with a diverging number of parameters . Ann. Statist. 32 : 928 – 961 .
   Web of Science ®Google Scholar
• Férre , L. ( 1998 ). Determing the dimension in sliced inverse regression and related methods . J. Amer. Statist. Assoc. 93 : 132 – 140 .
   Web of Science ®Google Scholar
• Hall , P. , Li , K. C. ( 1993 ). On almost linearity of low dimensional projection from high dimensional data . Ann. Statist. 21 : 867 – 889 .
   Web of Science ®Google Scholar
• Li , B. , Wang , S. L. ( 2007 ). On directional regression for dimension reduction . J. Amer. Statist. Assoc. 102 : 997 – 1008 .
   Web of Science ®Google Scholar
• Li , B. , Zha , H. , Chiaromonte , F. ( 2005 ). Contour regression: a general approach to dimension reduction . Ann. Statist. 33 : 1580 – 1616 .
   Web of Science ®Google Scholar
• Li , K. C. ( 1991 ). Sliced inverse regression for dimension reduction (with discussion) . J. Amer. Statist. Assoc. 86 : 316 – 342 .
   Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Li , K. C. , Duan , N. H. ( 1989 ). Regression analysis under link violation . Ann. Statist. 17 : 1009 – 1052 .
   Web of Science ®Google Scholar
• Li , Y. X. , Zhu , L. X. ( 2007 ). Asymptotics for sliced average variance estimation . Ann. Statist. 35 : 41 – 69 .
   Web of Science ®Google Scholar
• Loeve , M. ( 1978 ). Probability Theorey II. , 4th ed. New York : Springer-Verlag .
   Google Scholar
• Serfling , R. J. ( 1980 ). Approximation Theorems of Mathematical Statistics . New York : John Wiley & Sons Inc .
   Google Scholar
• Stute , W. , Zhu , L. X. ( 2005 ). Nonparametric checks for single-index models . Ann. Statist. 33 : 1048 – 1083 .
   Web of Science ®Google Scholar
• Zhu , L. X. , Fang , K. T. ( 1996 ). Asymptotics for the kernel estimates of sliced inverse regression . Ann. Statist. 24 : 1053 – 1067 .
   Web of Science ®Google Scholar
• Zhu , L. X. , Ng , K. W. ( 1995 ). Asymptotics of sliced inverse regression . Statist. Sinica 5 : 727 – 736 .
   Web of Science ®Google Scholar
• Zhu , L. P. , Zhu , L. X. ( 2007 ). On Kernel method for sliced average variance estimation . J. Multivariate Anal. 98 : 970 – 991 .
   Web of Science ®Google Scholar
• Zhu , L. P. , Zhu , L. X. ( 2008 ). Dimension reduction for conditional variance in regressions . Statist. Sinica 19 : 869 – 883 .
   Google Scholar
• Zhu , L. X. , Miao , B. Q. , Peng , H. ( 2006 ). Sliced inverse regression with large dimensional covariates . J. Amer. Statist. Assoc. 101 : 630 – 643 .
   Web of Science ®Google Scholar
• Zhu , L. X. , Ohtaki , M. , Li , Y. X. ( 2007 ). Hybrid methods of inverse regression based algorithms . Comp. Statist. Data. Anal. 51 : 2621 – 2635 .
   Web of Science ®Google Scholar