TY - JOUR
T1 - Efficiency loss and the linearity condition in dimension reduction
AU - Ma, Yanyuan
AU - Zhu, Liping
N1 - Funding Information:
Ma was supported by the National Science Foundation and National Institute of Neurological Disorders and Stroke, U.S.A. Zhu, the corresponding author, was supported by the Natural Science Foundation of China, Program for New Century Excellent Talents in University, the Innovation Program of Shanghai Municipal Education Commission and the Pujiang Project of the Science and Technology Commission of Shanghai Municipality. Zhu is also affiliated with the Key Laboratory of Mathematical Economics at Shanghai University of Finance and Economics.
PY - 2013/6
Y1 - 2013/6
N2 - Linearity, sometimes jointly with constant variance, is routinely assumed in the context of sufficient dimension reduction. It is well understood that, when these conditions do not hold, blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace. Surprisingly, we discover that even if these conditions do hold, using them will bring efficiency loss. This paradoxical phenomenon is illustrated through sliced inverse regression and principal Hessian directions. The efficiency loss also applies to other dimension reduction procedures. We explain this empirical discovery by theoretical investigation.
AB - Linearity, sometimes jointly with constant variance, is routinely assumed in the context of sufficient dimension reduction. It is well understood that, when these conditions do not hold, blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace. Surprisingly, we discover that even if these conditions do hold, using them will bring efficiency loss. This paradoxical phenomenon is illustrated through sliced inverse regression and principal Hessian directions. The efficiency loss also applies to other dimension reduction procedures. We explain this empirical discovery by theoretical investigation.
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U2 - 10.1093/biomet/ass075
DO - 10.1093/biomet/ass075
M3 - Article
AN - SCOPUS:84878080319
SN - 0006-3444
VL - 100
SP - 371
EP - 383
JO - Biometrika
JF - Biometrika
IS - 2
ER -