On regularization methods based on R 'enyi's pseudodistances for sparse\n high-dimensional linear regression models

2020/07/31 by Elena Castilla, Castilla, Elena, Abhik Ghosh +5
Engineering · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2007.15929

openalex publication_date 2020/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several regularization methods have been considered over the last decade for\nsparse high-dimensional linear regression models, but the most common ones use\nthe least square (quadratic) or likelihood loss and hence are not robust\nagainst data contamination. Some authors have overcome the problem of\nnon-robustness by considering suitable loss function based on divergence\nmeasures (e.g., density power divergence, gamma-divergence, etc.) instead of\nthe quadratic loss. In this paper we shall consider a loss function based on\nthe R 'enyi's pseudodistance jointly with non-concave penalties in order to\nsimultaneously perform variable selection and get robust estimators of the\nparameters in a high-dimensional linear regression model of non-polynomial\ndimensionality. The desired oracle properties of our proposed method are\nderived theoretically and its usefulness is illustustrated numerically through\nsimulations and real data examples.\n

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