Quantile-adaptive variable screening in ultra-high dimensional varying coefficient models |
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Authors: | Junying Zhang Zhiping Lu |
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Affiliation: | 1. School of Finance and Statistics, East China Normal University, Shanghai 200241, People's Republic of China;2. Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, People's Republic of China |
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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. |
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Keywords: | quantile regression varying-coefficient independent screening ultra-high dimension heterogeneous data variable selection dimensionality reduction |
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