Robust and consistent variable selection in high-dimensional generalized linear models

Avella‐Medina, Marco; Ronchetti, Elvezio

doi:10.1093/biomet/asx070

Cited by 29 publications

(17 citation statements)

References 51 publications

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“…However, one could expect a robust penalized estimator to behave as well as a robust oracle estimator at the model, while keeping its good robustness properties. We illustrate this point with a simulation study taken from Ref , where the theoretical properties are also discussed.…”

Section: High‐dimensional Statisticsmentioning

confidence: 89%

“…The adaptive lasso procedures used the weights

w_{j} = 1 true/ ((), {\overset{true^}{β}}_{j}^{(0)} + \frac{1}{n})

, where

{\overset{true^}{β}}^{(0)}

denotes the tuned lasso estimator. We used the coordinate descent algorithm described in Avella‐Medina and Ronchetti for the different versions of the lasso and we stop the algorithm when the tuning parameter gives models of size greater or equal 20. The selection of the tuning parameters is done by BIC.…”

Section: High‐dimensional Statisticsmentioning

confidence: 99%

“…The adaptive lasso procedures used the weights w j = the tuned lasso estimator. We used the coordinate descent algorithm described in Avella-Medina and Ronchetti99…”

mentioning

confidence: 99%

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Robust statistics: a selective overview and new directions

Medina

Ronchetti

2015

WIREs Computational Stats

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Classical statistics relies largely on parametric models. Typically, assumptions are made on the structural and the stochastic parts of the model and optimal procedures are derived under these assumptions. Standard examples are least squares estimators in linear models and their extensions, maximum-likelihood estimators and the corresponding likelihood-based tests, and generalized methods of moments (GMM) techniques in econometrics. Robust statistics deals with deviations from the stochastic assumptions and their dangers for classical estimators and tests and develops statistical procedures that are still reliable and reasonably efficient in the presence of such deviations. It can be viewed as a statistical theory dealing with approximate parametric models by providing a reasonable compromise between the rigidity of a strict parametric approach and the potential difficulties of interpretation of a fully nonparametric analysis. Many classical procedures are well known for not being robust. These procedures are optimal when the assumed model holds exactly, but they are biased and/or inefficient when small deviations from the model are present. The statistical results obtained from standard classical procedures on real data applications can therefore be misleading. In this paper we will give a brief introduction to robust statistics by reviewing some basic general concepts and tools and by showing how they can be used in data analysis to provide an alternative complementary analysis with additional useful information. In this study, we focus on robust statistical procedures based on M-estimators and tests because they provide a unified statistical framework that complements the classical theory. Robust procedures will be discussed for standard models, including linear models, general linear model, and multivariate analysis. Some recent developments in high-dimensional statistics will also be outlined.

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Section: High‐dimensional Statisticsmentioning

confidence: 89%

“…The adaptive lasso procedures used the weights

w_{j} = 1 true/ ((), {\overset{true^}{β}}_{j}^{(0)} + \frac{1}{n})

, where

{\overset{true^}{β}}^{(0)}

Section: High‐dimensional Statisticsmentioning

confidence: 99%

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Robust statistics: a selective overview and new directions

Medina

Ronchetti

2015

WIREs Computational Stats

Self Cite

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show abstract

“…Unlike Guo et al (2017), according to a natural point of view in robustness, we do not assume that the parameter space is a compact subset of R p , where p is the covariates dimension and weaker assumptions on the penalty are required. Besides, our results are not restricted to the LASSO or ADALASSO penalties as in Avella-Medina and Ronchetti (2018) or Guo et al (2017). Indeed, they are stated in a general penalty framework that allows to include not only the two penalties already mentioned but also SCAD and MCP penalties.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behaviour of penalized robust estimators in logistic regression when dimension increases

Bianco¹,

Boente²,

Chebi³

2022

Preprint

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Penalized M −estimators for logistic regression models have been previously study for fixed dimension in order to obtain sparse statistical models and automatic variable selection. In this paper, we derive asymptotic results for penalized M −estimators when the dimension p grows to infinity with the sample size n. Specifically, we obtain consistency and rates of convergence results, for a variety of penalties. Moreover, we prove that these estimators consistently select variables with probability tending to 1 and derive their asymptotic distribution.

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“…Some robust procedures are already available in the literature. Among others, Avella-Medina and Ronchetti (2017) proposed a robust penalized quasi-likelihood estimator for generalized linear models, Park and Konishi (2016) suggested a robust penalized logistic regression based on a weighted likelihood methodology, and Kurnaz et al (2018) adopted a trimmed elasticnet estimator for linear and logistic regression. However, none of these options satisfy the zero-sum constraint.…”

Section: Introductionmentioning

confidence: 99%

Robust logistic zero-sum regression for microbiome compositional data

Monti

Filzmoser

2021

Adv Data Anal Classif

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We introduce the Robust Logistic Zero-Sum Regression (RobLZS) estimator, which can be used for a two-class problem with high-dimensional compositional covariates. Since the log-contrast model is employed, the estimator is able to do feature selection among the compositional parts. The proposed method attains robustness by minimizing a trimmed sum of deviances. A comparison of the performance of the RobLZS estimator with a non-robust counterpart and with other sparse logistic regression estimators is conducted via Monte Carlo simulation studies. Two microbiome data applications are considered to investigate the stability of the estimators to the presence of outliers. Robust Logistic Zero-Sum Regression is available as an R package that can be downloaded at https://github.com/giannamonti/RobZS.

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Robust and consistent variable selection in high-dimensional generalized linear models

Cited by 29 publications

References 51 publications

Robust statistics: a selective overview and new directions

Robust statistics: a selective overview and new directions

Asymptotic behaviour of penalized robust estimators in logistic regression when dimension increases

Robust logistic zero-sum regression for microbiome compositional data

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