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<p>Nonparametric additive panel data models are powerful tools for capturing nonlinear relationships in fields such as econometrics and epidemiology. In high-dimensional settings, variable selection is crucial. To address this issue, we propose a variable selection method for high-dimensional nonparametric additive panel data models with fixed effects. The proposed method combines B-spline approximation with non-convex group penalties (specifically, group MCP and SCAD) and employs the forward orthogonal deviation transformation to eliminate fixed effects. This approach enables simultaneous variable selection and function estimation. The group descent algorithm and the BIC criterion are used for regularization. Theoretically, we establish the asymptotic properties of the proposed estimator under certain regularity conditions when the covariate dimension <i>p</i> can diverge with the sample size <i>n</i>, covering both <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p \le n\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p&gt; n\)</EquationSource> </InlineEquation> cases. Simulations and a real-data analysis demonstrate its finite-sample properties and practical utility.</p>

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Variable selection via non-convex group penalization for high-dimensional nonparametric additive panel data models with fixed effects

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Yiping Yang,
  • Ting Su,
  • Jun Zhang

摘要

Nonparametric additive panel data models are powerful tools for capturing nonlinear relationships in fields such as econometrics and epidemiology. In high-dimensional settings, variable selection is crucial. To address this issue, we propose a variable selection method for high-dimensional nonparametric additive panel data models with fixed effects. The proposed method combines B-spline approximation with non-convex group penalties (specifically, group MCP and SCAD) and employs the forward orthogonal deviation transformation to eliminate fixed effects. This approach enables simultaneous variable selection and function estimation. The group descent algorithm and the BIC criterion are used for regularization. Theoretically, we establish the asymptotic properties of the proposed estimator under certain regularity conditions when the covariate dimension p can diverge with the sample size n, covering both \(p \le n\) and \(p> n\) cases. Simulations and a real-data analysis demonstrate its finite-sample properties and practical utility.