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Quantile-adaptive variable screening in ultra-high dimensional varying coefficient models

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  • Junying Zhang
  • Riquan Zhang
  • Zhiping Lu

Abstract

The varying-coefficient model is an important nonparametric statistical model since it allows appreciable flexibility on the structure of fitted model. For ultra-high dimensional heterogeneous data it is very necessary to examine how the effects of covariates vary with exposure variables at different quantile level of interest. In this paper, we extended the marginal screening methods to examine and select variables by ranking a measure of nonparametric marginal contributions of each covariate given the exposure variable. Spline approximations are employed to model marginal effects and select the set of active variables in quantile-adaptive framework. This ensures the sure screening property in quantile-adaptive varying-coefficient model. Numerical studies demonstrate that the proposed procedure works well for heteroscedastic data.

Suggested Citation

  • Junying Zhang & Riquan Zhang & Zhiping Lu, 2016. "Quantile-adaptive variable screening in ultra-high dimensional varying coefficient models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 643-654, March.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:4:p:643-654
    DOI: 10.1080/02664763.2015.1072141
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    Cited by:

    1. Zhang, Shen & Zhao, Peixin & Li, Gaorong & Xu, Wangli, 2019. "Nonparametric independence screening for ultra-high dimensional generalized varying coefficient models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 37-52.
    2. Xiaolin Chen & Xiaojing Chen & Yi Liu, 2019. "A note on quantile feature screening via distance correlation," Statistical Papers, Springer, vol. 60(5), pages 1741-1762, October.

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