Sufficient dimension reduction using Hilbert-Schmidt independence criterion

By using Hilbert–Schmidt Independence Criterion, a sufficient dimension reduction method is proposed to estimate the directions in multiple-index models. A projection pursuit type of sufficient searching algorithm is introduced to reduce the computational complexity, as the original problem involves non-linear optimization over multidimensional Grassmann-manifold. A bootstrap procedure with additional jump point detection algorithm is used for determining the dimensionality. The proposed method demonstrates competitive performance compared with some well-known dimension reduction methods via simulation studies and an application to a real data.

[1]  H. Tong,et al.  Article: 2 , 2002, European Financial Services Law.

[2]  H. Zha,et al.  Contour regression: A general approach to dimension reduction , 2005, math/0508277.

[3]  Ker-Chau Li,et al.  On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma , 1992 .

[4]  R. Weiss,et al.  Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods , 2003 .

[5]  S. Weisberg,et al.  Comments on "Sliced inverse regression for dimension reduction" by K. C. Li , 1991 .

[6]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[7]  Bing Li,et al.  Successive direction extraction for estimating the central subspace in a multiple-index regression , 2008 .

[8]  Ker-Chau Li,et al.  On almost Linearity of Low Dimensional Projections from High Dimensional Data , 1993 .

[9]  Ker-Chau Li.  Sliced inverse regression for dimension reduction (with discussion) , 1991 .

[10]  A. Scott,et al.  A Cluster Analysis Method for Grouping Means in the Analysis of Variance , 1974 .

[11]  Bharath K. Sriperumbudur,et al.  Discussion of: Brownian distance covariance , 2009, 1010.0836.

[12]  Xiangrong Yin,et al.  Direction estimation in single-index models via distance covariance , 2013, J. Multivar. Anal..

[13]  Ker-Chau Li,et al.  Sliced Inverse Regression for Dimension Reduction , 1991 .

[14]  Nan Zhang,et al.  Direction Estimation in Single-Index Regressions via Hi lbert-Schmidt Independence Criterion , 2015 .

[15]  Yingcun Xia,et al.  Sliced Regression for Dimension Reduction , 2008 .

[16]  Yu Zhu,et al.  Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression , 2006 .

[17]  R. H. Moore,et al.  Regression Graphics: Ideas for Studying Regressions Through Graphics , 1998, Technometrics.

[18]  R. Cook.  Graphics for regressions with a binary response , 1996 .

[19]  Xiangrong Yin,et al.  Sufficient Dimension Reduction via Distance Covariance , 2016 .

[20]  R. Cook,et al.  Theory & Methods: Special Invited Paper: Dimension Reduction and Visualization in Discriminant Analysis (with discussion) , 2001 .