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

Xuming He, Lan Wang, Hyokyoung Grace Hong

Research output: Contribution to journalArticlepeer-review

141 Scopus citations

Abstract

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 quantilespecific information from heteroscedastic data.

Original languageEnglish (US)
Pages (from-to)342-369
Number of pages28
JournalAnnals of Statistics
Volume41
Issue number1
DOIs
StatePublished - Feb 1 2013

Keywords

  • Feature screening
  • High dimension
  • Polynomial splines
  • Quantile regression
  • Randomly censored data
  • Sure independence screening

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