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.

Xuming He

Lan Wang

Hyokyoung Grace Hong

The Annals of Statistics

《统计年鉴》旨在发表反映当代统计诸多方面的最高质量研究论文。主要强调重要性和独创性，而不是形式主义。该杂志旨在涵盖统计学的所有领域，尤其是数理统计学和应用与跨学科统计学。当然，许多最好的论文将涉及不止一个这些一般领域，因为统计学科深深植根于数学和实质性科学领域。

The Annals of Statistics aims to publish high-quality research papers that reflect various aspects of contemporary statistics. The journal emphasizes the importance and originality of the research rather than formalism. It covers all areas of statistics, particularly mathematical statistics and applied and interdisciplinary statistics. Many of the best papers will involve more than one of these general areas, as the field of statistics is deeply rooted in mathematics and substantive sciences.

《Annals of Statistics》旨在发表反映当代统计学各个方面的高质量研究论文。该期刊主要强调研究的重要性和独创性，而非形式主义。它涵盖统计学的所有领域，特别是数理统计和应用统计及跨学科统计。许多优秀的论文往往涉及多个领域，因为统计学与数学及其他实质性科学领域密切相关。

Annals of Statistics

Ann. Statist.

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

It is proved that the sure screening property remains valid when the response variable is subject to random right censoring, and the quantile-adaptive framework can naturally handle censored data arising in survival analysis.

Category	Quartile
数学	1
数学, 统计学与概率论	1

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

ivySCI AI Smartly Parses PDF, Answers Researchers' Questions, and Helps You Understand Papers in Seconds

Journal Info

Category	Quartile
STATISTICS & PROBABILITY	1