Multitask Quantile Regression under the Transnormal Model

By Jianqing Fan, Lingzhou Xue, Hui Zou. 2016

33 citations recorded by the source corpus.

ABSTRACT 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 ℓ1 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.

Subfields: Artificial Intelligence, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Lingzhou Xue
2. Kari Torkkola
3. Ruofeng Wen
4. Jiawei Yao
5. Jianqing Fan
6. Jinchi Lv
7. Yingying Fan
8. Hui Zou

In Statistics and Probability

1. Lingzhou Xue
2. Jiawei Yao
3. Jianqing Fan
4. Kari Torkkola
5. Ruofeng Wen
6. Clifford Lam
7. Yuan Liao
8. Hui Zou

Citations in the corpus

• Deep Generative Quantile-Copula Models for Probabilistic Forecasting (2019, methodology): “AIQN pairs the univariate generative quantile net with an autoregressive model extending to the multivariate case, but suffers all the disadvantages of autoregressive models (e.g. error accumulation).Fan et al, 2016proposed a trans-normal model by using the empirical marginal quantiles to transform ”
• Sufficient Forecasting Using Factor Models (2015, methodology): “Thus, with covariates Z, the sufficient forecasting achieves a faster rate of convergence by using the projected PCA (Fan et al., 2016).”
• Inverse Moment Methods for Sufficient Forecasting Using High-Dimensional Predictors (2016, unknown): “University and Citadel LLC Abstract We consider forecasting a single time series using high-dimensional predictors in the presence of a possible nonlinear forecast function. The sucient forecasting (Fan et al., 2016) used sliced inverse regression to estimate lower-dimensional sucient indices for fo”