Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data

By Xuming He, Lan Wang, Hyokyoung Grace Hong. 2013

260 citations recorded by the source corpus.

We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus making it more flexible to accommodate heterogeneity; (2) it is model-free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space. Our nonlinear independence screening procedure employs spline approximations to model the marginal effects at a quantile level of interest. Under appropriate conditions on the quantile functions without requiring the existence of any moments, the new procedure is shown to enjoy the sure screening property in ultra-high dimensions. Furthermore, the quantile-adaptive framework can naturally handle censored data arising in survival analysis. We prove that the sure screening property remains valid when the response variable is subject to random right censoring. Numerical studies confirm the fine performance of the proposed method for various semiparametric models and its effectiveness to extract quantile-specific information from heteroscedastic data.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/11d852fd1fb8781e03c0d4eb96468e66fb1c8f62

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. Yuanshan Wu
2. Guosheng Yin
3. Byeong U. Park
4. Hohsuk Noh
5. Eun Ryung Lee

In Statistics and Probability

1. Eun Ryung Lee
2. Yuanshan Wu
3. Guosheng Yin
4. Byeong U. Park
5. Hohsuk Noh
6. James W. Taylor

Citations in the corpus

• Conditional quantile screening in ultrahigh-dimensional heterogeneous data (2015, methodology): “…of Li et al. (2012b); Q-SIS, proposed conditional quantile sure independent screening approach; QaSIS, quantile adaptive sure independent screening of He et al. (2013); MDC-SISQ, martingale difference correlation sure independent screening of Shao & Zhang (2014); cens., censored data…”
• Model Selection via Bayesian Information Criterion for Quantile Regression Models (2014, methodology): “(2012). The condition (ii) of (A2) is the sparse Riesz condition assumed by Zhang and Huang (2008) and Chen and Chen (2008), which is one of the well-known conditions to deal with the situation where the number of regression coefficients exceeds the number of observations (p > n).”