Robust Variable Selection in High-dimensional Nonparametric Additive Model

2025/05/06 by Suneel Babu Chatla, Abhijit Mandal, Chatla, Suneel Babu +1
Mathematics · #62G05 #62G35 #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2505.04009

openalex publication_date 2025/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Additive models belong to the class of structured nonparametric regression models that do not suffer from the curse of dimensionality. Finding the additive components that are nonzero when the true model is assumed to be sparse is an important problem, and it is well studied in the literature. The majority of the existing methods focused on using the L₂ loss function, which is sensitive to outliers in the data. We propose a new variable selection method for additive models that is robust to outliers in the data. The proposed method employs a nonconcave penalty for variable selection and considers the framework of B-splines and density power divergence loss function for estimation. The loss function produces an M-estimator that down weights the effect outliers. Our asymptotic results are derived under the sub-Weibull assumption, which allows the error distribution to have an exponentially heavy tail. Under regularity conditions, we show that the proposed method achieves the optimal convergence rate. In addition, our results include the convergence rates for sub-Gaussian and sub-Exponential distributions as special cases. We numerically validate our theoretical findings using simulations and real data analysis.

Citations

• Robust Density Power Divergence Estimates for Panel Data Models
• A robust spline approach in partially linear additive models
• Robust Variable Selection Criteria for the Penalized Regression
• The Bennett-Orlicz norm
• Additive Models with Trend Filtering
• Marginal integration M-estimators for additive models
• Generalized Additive Model Selection
• A Selective Review of Group Selection in High-Dimensional Models
• Nearly unbiased variable selection under minimax concave penalty
• Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models
• Non-Concave Penalized Likelihood with NP-Dimensionality
• Sparse Additive Models
• A Statistical View of Some Chemometrics Regression Tools

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