Robust estimation of dimension reduction space

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractMost 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 sufficiently 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.

An adaptive estimation of MAVE

“…Xia and Härdle (2006) applied MAVE to partially linear single-index models so that no √ n-consistent pilot estimator is needed and the choice of bandwidth is more flexible. Čížek and Härdle (2006) proposed a robust version by replacing the least squares with local L-or M-estimation so that MAVE is robust to outliers in the dependent variable. Wang and Yin (2008) incorporated shrinkage estimation to MAVE so that variable selection and dimension reduction can be achieved simultaneously.…”

A new sliced inverse regression method for multivariate response

“…Hessian directions (see for instance Li (1992) or Cook (1998)), sliced average variance estimation (see for details Cook (2000), Prendergast (2007) or Shao et al (2009)) and minimum average variance estimation (Xia et al (2002), Cížek and Härdle (2006)). For the sake of simplicity, we shall only focus here on the SIR approach which is based on a property of the first moment of the inverse distribution of x given y.…”

Robust variable selection through MAVE

“…However, one might further speed up the computation based on the 7 one-step M-estimation as discussed in Fan and Jiang (1999), Welsch andRonchetti (2002), andČížek andH¨ rdle (2006). Therefore, we can just simply run one iteration from Step 1 to…”