Variable Selection in High-dimensional Varying-coefficient Models with Global Optimality Public Deposited

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  • The varying-coefficient model is flexible and powerful for modeling the dynamic changes of regression coefficients. It is important to identify significant covariates associated with response variables, especially for high-dimensional settings where the number of covariates can be larger than the sample size. We consider model selection in the high-dimensional setting and adopt difference convex programming to approximate the L₀ penalty, and we investigate the global optimality properties of the varying-coefficient estimator. The challenge of the variable selection problem here is that the dimension of the nonparametric form for the varying-coefficient modeling could be infinite, in addition to dealing with the high-dimensional linear covariates. We show that the proposed varying-coefficient estimator is consistent, enjoys the oracle property and achieves an optimal convergence rate for the non-zero nonparametric components for high-dimensional data. Our simulations and numerical examples indicate that the difference convex algorithm is efficient using the coordinate decent algorithm, and is able to select the true model at a higher frequency than the least absolute shrinkage and selection operator (LASSO), the adaptive LASSO and the smoothly clipped absolute deviation (SCAD) approaches.
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  • Xue, L., & Qu, A. (2012). Variable selection in high-dimensional varying-coefficient models with global optimality. Journal of Machine Learning Research, 13, 1973-1998.
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  • description.provenance : Submitted by Deborah Campbell (deborah.campbell@oregonstate.edu) on 2013-02-06T21:45:19Z No. of bitstreams: 1 XueLanStatisticsVariableSelectionHigh.pdf: 256723 bytes, checksum: abac2ea296b44af5fe4dc390b415d467 (MD5)
  • description.provenance : Made available in DSpace on 2013-02-06T23:04:33Z (GMT). No. of bitstreams: 1 XueLanStatisticsVariableSelectionHigh.pdf: 256723 bytes, checksum: abac2ea296b44af5fe4dc390b415d467 (MD5) Previous issue date: 2012-06
  • description.provenance : Approved for entry into archive by Deborah Campbell(deborah.campbell@oregonstate.edu) on 2013-02-06T23:04:33Z (GMT) No. of bitstreams: 1 XueLanStatisticsVariableSelectionHigh.pdf: 256723 bytes, checksum: abac2ea296b44af5fe4dc390b415d467 (MD5)

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