Sparse Unit-Sum Regression

Nick Koning; Paul Bekker

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arXiv · 1907.04620

Sparse Unit-Sum Regression

Nick Koning·Paul Bekker

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Abstract

This paper considers sparsity in linear regression under the restriction that the regression weights sum to one. We propose an approach that combines $\ell_0$- and $\ell_1$-regularization. We compute its solution by adapting a recent methodological innovation made by Bertsimas et al. (2016) for $\ell_0$-regularization in standard linear regression. In a simulation experiment we compare our approach to $\ell_0$-regularization and $\ell_1$-regularization and find that it performs favorably in terms of predictive performance and sparsity. In an application to index tracking we show that our approach can obtain substantially sparser portfolios compared to $\ell_1$-regularization while maintaining a similar tracking performance.

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Nick Koning, Paul Bekker. 2019-07-10. Sparse Unit-Sum Regression. https://arxiv.org/abs/1907.04620

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