TY - JOUR
T1 - On splines approximation for sliced average variance estimation
AU - Yu, Zhou
AU - Zhu, Li-Ping
AU - Zhu, Li-Xing
N1 - Funding Information:
The first author was supported by National Social Science Foundation of China (08CTJ001), and the second author was supported by a scholarship under the State Scholarship Fund ([2007]3020). The third author was supported by a RGC grant from the Research Grants Council of Hong Kong, Hong Kong, China. The authors thank the editor, the associate editor and the referees for their constructive comments and suggestions that led to a significant improvement in presentation of the early draft.
PY - 2009/4/1
Y1 - 2009/4/1
N2 - To avoid the inconsistency and slow convergence rate of the slicing estimator of the sliced average variance estimation (SAVE), particularly in the continuous response cases, we suggest B-spline approximation that can make the estimator sqrt(n) consistent and keeps the spirit of easy implementation that the slicing estimation shares. Compared with kernel estimation that has been used in the literature, B-spline approximation is of higher accuracy and is easier to implement. To estimate the structural dimension of the central dimension reduction space, a modified Bayes information criterion is suggested, which makes the leading term and the penalty term comparable in magnitude. This modified criterion can help to enhance the efficacy of estimation. The methodologies and theoretical results are illustrated through an application to the horse mussel data and simulation comparisons with existing methods by simulations.
AB - To avoid the inconsistency and slow convergence rate of the slicing estimator of the sliced average variance estimation (SAVE), particularly in the continuous response cases, we suggest B-spline approximation that can make the estimator sqrt(n) consistent and keeps the spirit of easy implementation that the slicing estimation shares. Compared with kernel estimation that has been used in the literature, B-spline approximation is of higher accuracy and is easier to implement. To estimate the structural dimension of the central dimension reduction space, a modified Bayes information criterion is suggested, which makes the leading term and the penalty term comparable in magnitude. This modified criterion can help to enhance the efficacy of estimation. The methodologies and theoretical results are illustrated through an application to the horse mussel data and simulation comparisons with existing methods by simulations.
KW - Asymptotic normality
KW - B-spline
KW - Bayes information criterion
KW - Dimension reduction
KW - Sliced average variance estimation
KW - Structural dimension
UR - http://www.scopus.com/inward/record.url?scp=57749205197&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2008.07.017
DO - 10.1016/j.jspi.2008.07.017
M3 - Journal article
AN - SCOPUS:57749205197
SN - 0378-3758
VL - 139
SP - 1493
EP - 1505
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 4
ER -