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February 2007 Asymptotics for sliced average variance estimation
Yingxing Li, Li-Xing Zhu
Ann. Statist. 35(1): 41-69 (February 2007). DOI: 10.1214/009053606000001091


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 $\sqrt{n}$ consistency even when each slice contains only two data points. However, SAVE cannot be $\sqrt{n}$ 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 $\sqrt{n}$ consistent. In contrast, when the response is discrete and takes finite values, $\sqrt{n}$ 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.


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Yingxing Li. Li-Xing Zhu. "Asymptotics for sliced average variance estimation." Ann. Statist. 35 (1) 41 - 69, February 2007.


Published: February 2007
First available in Project Euclid: 6 June 2007

zbMATH: 1114.62053
MathSciNet: MR2332268
Digital Object Identifier: 10.1214/009053606000001091

Primary: 62E20 , 62G08 , 62H99

Keywords: asymptotic , convergence rate , Dimension reduction , sliced average variance estimation

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 1 • February 2007
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