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Nonlinear dimension reduction for conditional quantiles

Christou, Eliana, Settle, Annabel and Artemiou, Andreas 2021. Nonlinear dimension reduction for conditional quantiles. Advances in Data Analysis and Classification 10.1007/s11634-021-00439-6
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In practice, data often display heteroscedasticity, making quantile regression (QR) a more appropriate methodology. Modeling the data, while maintaining a flexible nonparametric fitting, requires smoothing over a high-dimensional space which might not be feasible when the number of the predictor variables is large. This problem makes necessary the use of dimension reduction techniques for conditional quantiles, which focus on extracting linear combinations of the predictor variables without losing any information about the conditional quantile. However, nonlinear features can achieve greater dimension reduction. We, therefore, present the first nonlinear extension of the linear algorithm for estimating the central quantile subspace (CQS) using kernel data. First, we describe the feature CQS within the framework of reproducing kernel Hilbert space, and second, we illustrate its performance through simulation examples and real data applications. Specifically, we emphasize on visualizing various aspects of the data structure using the first two feature extractors, and we highlight the ability to combine the proposed algorithm with classification and regression linear algorithms. The results show that the feature CQS is an effective kernel tool for performing nonlinear dimension reduction for conditional quantiles.

Item Type: Article
Date Type: Published Online
Status: In Press
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer Verlag (Germany)
ISSN: 1862-5347
Date of First Compliant Deposit: 9 March 2021
Date of Acceptance: 8 March 2021
Last Modified: 13 Apr 2021 14:01

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