Jing Zhou, Gerda Claeskens, Jelena Bradic
arXiv 12 Jun 2020 · Mathematics — Statistics Theory · publishedElectronic Journal of Statistics (2020) · 3 citations (OpenAlex)
arXiv:2006.07457 · PDF · DOI · OpenAlex · Extracted main text
Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory identifies equivalence between model-averaged and composite quantile estimation. However, little to nothing is known about such equivalence between methods that encourage sparsity. This paper provides a toolbox to further study robustness in these settings and focuses on prediction. In particular, we study optimally weighted model-averaged as well as composite $l_1$-regularized estimation. Optimal weights are determined by minimizing the asymptotic mean squared error. This approach incorporates the effects of regularization, without the assumption of perfect selection, as is often used in practice. Such weights are then optimal for prediction quality. Through an extensive simulation study, we show that no single method systematically outperforms others. We find, however, that model-averaged and composite quantile estimators often outperform least-squares methods, even in the case of Gaussian model noise. Real data application witnesses the method's practical use through the reconstruction of compressed audio signals.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Donoho, D. and Montanari, A (2016) High dimensional robust m-estimation: Asymptotic variance via approximate message passing | 0.935 | 11 | 5 | 82% |
| 2 | Bloznelis, D., Claeskens, G., and Zhou, J (2019) Composite versus model-averaged quantile regression self | 0.928 | 4 | 3 | 100% |
| 3 | Bradic, J., Fan, J., and Wang, W (2011) Penalized composite quasi-likelihood for ultrahigh dimensional variable selection self | 0.928 | 4 | 3 | 100% |
| 4 | Bradic, J (2016) Robustness in sparse high-dimensional linear models: Relative efficiency and robust approximate message passing self | 0.881 | 19 | 8 | 68% |
| 5 | Bayati, M., Erdogdu, M., and Montanari, A (2013) Estimating lasso risk and noise level | 0.811 | 5 | 2 | 80% |
| 6 | Bayati, M. and Montanari, A (2011) The dynamics of message passing on dense graphs, with applications to compressed sensing | 0.652 | 36 | 6 | 28% |
| 7 | Bates, J. M. and Granger, C. W. J (1969) The combination of forecasts | 0.644 | 2 | 2 | 100% |
| 8 | Koenker, R (2005) Quantile Regression | 0.644 | 2 | 2 | 100% |
| 9 | Bayati, M. and Montanari, A (2011) The lasso risk for gaussian matrices | 0.644 | 2 | 2 | 100% |
| 10 | Donoho, D., Maleki, A., and Montanari, A (2009) Message-passing algorithms for compressed sensing | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 38 scored citations.