TY - JOUR
T1 - Principal minimax support vector machine for sufficient dimension reduction with contaminated data
AU - Zhou, Jingke
AU - ZHU, Lixing
N1 - Funding Information:
The authors thank the associate editor and two referees for their insightful and thorough suggestions and comments which led to a significant improvement of an early manuscript. The research described herein was supported by a GRF grant from the University Grants Council of Hong Kong .
PY - 2016/2/14
Y1 - 2016/2/14
N2 - To make sufficient dimension reduction methods be able to handle contaminated data, a principal minimax support vector machine is suggested to identifying the central subspace. For sparse sufficient dimension reduction, this method of adaptive elastic net type is suggested to make estimation more accurate. The methods are extended to deal with transformed sufficient dimension reduction against contaminated data. The asymptotic unbiasedness and exhaustiveness are proved from the viewpoint of sufficient dimension reduction, and the sparseness and model selection consistency are showed from the viewpoint of variable selection. Simulations and real data analysis are conducted to examine the finite sample performances of the proposed methods.
AB - To make sufficient dimension reduction methods be able to handle contaminated data, a principal minimax support vector machine is suggested to identifying the central subspace. For sparse sufficient dimension reduction, this method of adaptive elastic net type is suggested to make estimation more accurate. The methods are extended to deal with transformed sufficient dimension reduction against contaminated data. The asymptotic unbiasedness and exhaustiveness are proved from the viewpoint of sufficient dimension reduction, and the sparseness and model selection consistency are showed from the viewpoint of variable selection. Simulations and real data analysis are conducted to examine the finite sample performances of the proposed methods.
KW - Minimax robust support vector machines
KW - Robust sufficient dimension reduction
KW - Sparse sufficient dimension reduction
KW - Transformed sufficient dimension reduction
UR - http://www.scopus.com/inward/record.url?scp=84941287210&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2015.06.011
DO - 10.1016/j.csda.2015.06.011
M3 - Journal article
AN - SCOPUS:84941287210
SN - 0167-9473
VL - 94
SP - 33
EP - 48
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
ER -