Sufficient dimension reduction based on an ensemble of minimum average variance estimators

By Xiangrong Yin, Bing Li. 2011

85 citations recorded by the source corpus.

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box―Cox transformations and wavelet basis. The ensemble estimators exhaustively estimate the central subspace without imposing restrictive conditions on the predictors, and have the same convergence rate as the minimum average variance estimates. They are flexible and easy to implement, and allow repeated use of the available sample, which enhances accuracy. They are applicable to both univariate and multivariate responses in a unified form. We establish the consistency and convergence rate of these estimators, and the consistency of a cross validation criterion for order determination. We compare the ensemble estimators with other estimators in a wide variety of models, and establish their competent performance.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/732caf8f825dec66db94904ba101db2f643c1ba1

How researchers see this paper

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

In Finance

1. Haileab Hilafu
2. Wenhui Sheng
3. Xiangrong Yin

In Statistics and Probability

1. Haileab Hilafu
2. Wenhui Sheng
3. Xiangrong Yin
4. Yingcun Xia
5. Bing Li
6. Lixing Zhu

Citations in the corpus

• Sequential sufficient dimension reduction for large p, small n problems (2015, methodology): “Although we agree with this, we borrow the ensemble idea from Yin and Li (2011) to provide a partial remedy (see limited evidence in the on-line supplementary file).”
• Sufficient Dimension Reduction via Distance Covariance (2016, methodology): “…ones are minimum average variance estimation method (MAVE; Xia et al. 2002), sliced regression (SR; Wang and Xia 2008), and ensemble approach (Yin and Li 2011); however, these methods used nonparametric tools, which implicitly require the predictors to be continuous and the link Wenhui Sheng…”