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August 2022 Conditional variance estimator for sufficient dimension reduction
Lukas Fertl, Efstathia Bura
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Bernoulli 28(3): 1862-1891 (August 2022). DOI: 10.3150/21-BEJ1402

Abstract

Conditional Variance Estimation (CVE) is a novel sufficient dimension reduction (SDR) method for additive error regressions with continuous predictors and link function. It operates under the assumption that the predictors can be replaced by a lower dimensional projection without loss of information. Conditional Variance Estimation is fully data driven, does not require the restrictive linearity and constant variance conditions, and is not based on inverse regression as the majority of moment and likelihood based sufficient dimension reduction methods. CVE is shown to be consistent and its objective function to be uniformly convergent. CVE outperforms the mean average variance estimation, (MAVE), its main competitor, in several simulation settings, remains on par under others, while it always outperforms inverse regression based linear SDR methods, such as Sliced Inverse Regression.

Acknowledgements

The authors gratefully acknowledge the support of the Austrian Science Fund (FWF P 30690-N35) and thank Daniel Kapla for his programming assistance and Tijana Levajkovic and Michael Messer for their thorough reading and suggestions. Daniel Kapla co-authored the CVarE R package that implements the proposed method. We also thank two reviewers and an associate editor, whose suggestions helped us to improve the paper.

Citation

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Lukas Fertl. Efstathia Bura. "Conditional variance estimator for sufficient dimension reduction." Bernoulli 28 (3) 1862 - 1891, August 2022. https://doi.org/10.3150/21-BEJ1402

Information

Received: 1 January 2021; Published: August 2022
First available in Project Euclid: 25 April 2022

Digital Object Identifier: 10.3150/21-BEJ1402

Keywords: Dimension reduction , mean subspace , minimum average variance estimation , nonparametric , regression

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Vol.28 • No. 3 • August 2022
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