Robust estimation of dimension reduction space
Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions. We show that the recently proposed methods by Xia et al. (2002) can be made robust in such a way that preserves all advantages of the original approach. Their extension based on the local one-step M-estimators is su±ciently robust to outliers and data from heavy tailed distributions, it is relatively easy to implement, and surprisingly, it performs as well as the original methods when applied to normally distributed data.
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- Yingcun Xia & Howell Tong & W. K. Li & Li-Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410.
- Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
- Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
- Qiwei Yao & Howell Tong, 1994. "On subset selection in non-parametric stochastic regression," LSE Research Online Documents on Economics 6409, London School of Economics and Political Science, LSE Library.
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