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Multitask Quantile Regression Under the Transnormal Model
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DOI：10.1080/01621459.2015.1113973.png)
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Abstract
En 中文
We consider estimating multitask quantile regression under the transnormal model, with focus on high dimensional setting. We derive a surprisingly simple closed-form solution through rank-based covariance regularization. In particular, we propose the rank-based l(1), penalization with positive-definite constraints for estimating sparse covariance matrices, and the rank-based banded Cholesky decomposition regularization for estimating banded precision matrices. By taking advantage of the alternating direction method of multipliers, nearest correlation matrix projection is introduced that inherits sampling properties of the unprojected one. Our work combines strengths of quantile regression and rank-based covariance regularization to simultaneously deal with nonlinearity and nonnormality for high-dimensional regression. Furthermore, the proposed method strikes a good balance between robustness and efficiency, achieves the oracle-like convergence rate, and provides the provable prediction interval under the high-dimensional setting. The finite-sample performance of the proposed method is also examined. The performance of our proposed rank-based method is demonstrated in a real application to analyze the protein mass spectroscopy data. Supplementary materials for this article are available online.
Keywords:
Copula model
Optimal transformation
Rank correlation
Cholesky decomposition
Quantile regression
Prediction interval
Alternating direction method of multipliers
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