TY - JOUR
T1 - Asymptotics for sliced average variance estimation
AU - Li, Yingxing
AU - Zhu, Lixing
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2007/2
Y1 - 2007/2
N2 - In this paper, we systematically study the consistency of sliced average variance estimation (SAVE). The findings reveal that when the response is continuous, the asymptotic behavior of SAVE is rather different from that of sliced inverse regression (SIR). SIR can achieve √n consistency even when each slice contains only two data points. However, SAVE cannot be √n consistent and it even turns out to be not consistent when each slice contains a fixed number of data points that do not depend on n, where n is the sample size. These results theoretically confirm the notion that SAVE is more sensitive to the number of slices than SIR. Taking this into account, a bias correction is recommended in order to allow SAVE to be √n consistent. In contrast, when the response is discrete and takes finite values, √n consistency can be achieved. Therefore, an approximation through discretization, which is commonly used in practice, is studied. A simulation study is carried out for the purposes of illustration.
AB - In this paper, we systematically study the consistency of sliced average variance estimation (SAVE). The findings reveal that when the response is continuous, the asymptotic behavior of SAVE is rather different from that of sliced inverse regression (SIR). SIR can achieve √n consistency even when each slice contains only two data points. However, SAVE cannot be √n consistent and it even turns out to be not consistent when each slice contains a fixed number of data points that do not depend on n, where n is the sample size. These results theoretically confirm the notion that SAVE is more sensitive to the number of slices than SIR. Taking this into account, a bias correction is recommended in order to allow SAVE to be √n consistent. In contrast, when the response is discrete and takes finite values, √n consistency can be achieved. Therefore, an approximation through discretization, which is commonly used in practice, is studied. A simulation study is carried out for the purposes of illustration.
KW - Asymptotic
KW - Convergence rate
KW - Dimension reduction
KW - Sliced average variance estimation
UR - http://www.scopus.com/inward/record.url?scp=49449119125&partnerID=8YFLogxK
U2 - 10.1214/009053606000001091
DO - 10.1214/009053606000001091
M3 - Journal article
AN - SCOPUS:49449119125
SN - 0090-5364
VL - 35
SP - 41
EP - 69
JO - Annals of Statistics
JF - Annals of Statistics
IS - 1
ER -