Nonlinear dimension reduction for conditional quantiles
| Autor: | Andreas Artemiou, Annabel Settle, Eliana Christou |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Heteroscedasticity Statistics::Theory Computer science Applied Mathematics Dimensionality reduction 05 social sciences 01 natural sciences Computer Science Applications Quantile regression 010104 statistics & probability Kernel (statistics) 0502 economics and business Feature (machine learning) Statistics::Methodology 0101 mathematics QA Algorithm Smoothing 050205 econometrics Reproducing kernel Hilbert space Quantile |
| ISSN: | 1862-5347 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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