Dimension reduction for nonelliptically distributed predictors
By Bing Li, Yuexiao Dong. 2009
121 citations recorded by the source corpus.
Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately. For example, a typical dimension reduction method would require the predictor to have elliptical or even multivariate normal distribution. In this paper, we reformulate the commonly used dimension reduction methods, via the notion of "central solution space," so as to circumvent the requirements of such strong assumptions, while at the same time preserve the desirable properties of the classical methods, such as √n-consistency and asymptotic normality. Imposing elliptical distributions or even stronger assumptions on predictors is often considered as the necessary tradeoff for overcoming the "curse of dimensionality," but the development of this paper shows that this need not be the case. The new methods will be compared with existing methods by simulation and applied to a data set.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/2547c6eb52fa906fb8a7ca70b3fa661a2f8b8b28
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In Artificial Intelligence
In Statistics and Probability
Citations in the corpus
- On estimation efficiency of the central mean subspace (2014, methodology): “…test procedure in Cook and Li (2004), the crossvalidation procedure in Xia et al. (2002) and Xia (2007), the Bayesian information criterion BIC type of criterion in Zhu et al. (2006) and the bootstrap procedure in Ye and Weiss (2003), Li and Dong (2009), Dong and Li (2010), Ma and Zhu (2012), etc.”