International Journal of Mathematics Trends and Technology
Volume 70 | Issue 1 | Year 2024 | Article Id. IJMTT-V70I1P104 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I1P104
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 01 Dec 2023 | 04 Jan 2024 | 17 Jan 2024 | 31 Jan 2024 |
This paper consider modal regression in varying coefficient model with high dimensionality under a sparsity
assumption. We apply the B-spline basis to approximate the varying coefficient functions. First, we demonstrate the
convergence rates of the oracle estimator when the nonzero components are known in advance, but their numbers is
diverging with the sample size. Then, we propose a nonconvex group SCAD penalized estimator and derive its oracle
property under some regularity conditions. That is, under mild conditions, we prove that the oracle estimator is a local
solution of the group SCAD penalized estimator of modal regression in varying coefficient model with high dimensionality.
Furthermore, we address issues of numerical implementation and of data adaptive choice of the tuning parameters. Some
Monte Carlo simulations are provided to corroborate our theoretical findings in finite samples.
High dimensionality, Modal regression, Oracle property, Varying coefficient model, Variable selection.
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Zhaoliang Wang, Suting Zhang, "Modal Regression for Varying Coefficient Model in High Dimensions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 1, pp. 27-39, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I1P104
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