Asymptotics for sliced average variance estimation

By Yingxing Li, Li-Xing Zhu. 2007

88 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a3b98febf009ec3292324fc20cac538aa8360b8d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Jane-ling Wang
2. Lixing Zhu
3. Liugen Xue
4. Y. S. Chong

In Statistics and Probability

1. Liugen Xue
2. Lixing Zhu
3. Jane-ling Wang
4. Y. S. Chong
5. H. Muller
6. Lan Wang
7. Fang Yao
8. Jeng-Min Chiou

Citations in the corpus

• Estimation for a partial-linear single-index model (2009, methodology): “Li and Zhu (2007) further show that, when including a bias-correction and under a condition almost equivalent to normality of X, sliced average variance estimation [SAVE, see Cook and Weisberg (1991)] performs similarly.”