Inference robust to outliers with <i>ℓ</i><sub>1</sub>-norm penalization

Beyhum, Jad

doi:10.1051/ps/2020014

Cited by 4 publications

(8 citation statements)

References 35 publications

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“…Censoring poses additional challenges because T i is not observed for some i. It is well known that 1 -norm penalization allows to build robust estimators ( [21,5]). In [24], Stute proposes a simple estimator for censored regression.…”

Section: Main Estimatormentioning

confidence: 99%

“…for any b ∈ R p and, therefore, β = β( α) when there is a unique solution to the minimization program (5). Hence, when (X w ) X w is positive definite, we have…”

Section: Main Estimatormentioning

confidence: 99%

“…[10,21,16,15,8,11,7]). In this setup, [5] develops estimation results similar to those of the present paper but does not allow for censoring and does not study the two-step procedure.…”

Section: Introductionmentioning

confidence: 98%

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Robust censored regression with l1-norm regularization

Beyhum¹,

Keilegom²

2021

Preprint

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This paper considers inference in a linear regression model with random right censoring and outliers. The number of outliers can grow with the sample size while their proportion goes to zero. The model is semiparametric and we make only very mild assumptions on the distribution of the error term, contrary to most other existing approaches in the literature. We propose to penalize the estimator proposed by Stute for censored linear regression by the 1 -norm. We derive rates of convergence and establish asymptotic normality of the estimator of the regression coefficients. Our estimator has the same asymptotic variance as Stute's estimator in the censored linear model without outliers. Hence, there is no loss of efficiency as a result of robustness. Tests and confidence sets can therefore rely on the theory developed by Stute. The outlined procedure is also computationally advantageous, since it amounts to solving a convex optimization program. We also propose a second estimator which uses the proposed penalized Stute estimator as a first step to detect outliers. It has similar theoretical properties but better performance in finite samples as assessed by simulations.

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Section: Main Estimatormentioning

confidence: 99%

“…for any b ∈ R p and, therefore, β = β( α) when there is a unique solution to the minimization program (5). Hence, when (X w ) X w is positive definite, we have…”

Section: Main Estimatormentioning

confidence: 99%

See 1 more Smart Citation

Robust censored regression with l1-norm regularization

Beyhum¹,

Keilegom²

2021

Preprint

Self Cite

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“…[9] elaborates on how to choose λ k β according to (i). Lemma 2.3 and Corollary 2.4. in [11] provide guidance on how to pick λ γ k under this constraint. Condition (ii) states that the extended restricted eigenvalue is bounded from below with probability approaching 1.…”

Section: Rate Of Convergence Of the First Step Estimatormentioning

confidence: 99%

“…These works do not provide inference results. In this setup, [11] shows that a variant of the square-root lasso estimator is asymptotically normal and efficient. The present paper can be seen as an extension of this result in a high-dimensional context.…”

Section: Introductionmentioning

confidence: 99%

High-dimensional inference robust to outliers with l1-norm penalization

Beyhum¹

2020

Preprint

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This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their proportion goes to 0. We propose a two-step procedure for inference on the coefficients of a fixed subset of regressors. The first step is a based on several square-root lasso ℓ 1 -norm penalized estimators, while the second step is the ordinary least squares estimator applied to a well chosen regression. We establish asymptotic normality of the two-step estimator. The proposed procedure is efficient in the sense that it attains the semiparametric efficiency bound when applied to the model without outliers under homoscedasticity. This approach is also computationally advantageous, it amounts to solving a finite number of convex optimization programs.

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Robust censored regression with $$\ell _1$$-norm regularization

Beyhum

Keilegom

2022

TEST

Self Cite

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This paper considers inference in a linear regression model with random right censoring and outliers. The number of outliers can grow with the sample size while their proportion goes to zero. The model is semiparametric and we make only very mild assumptions on the distribution of the error term, contrary to most other existing approaches in the literature. We propose to penalize the estimator proposed by Stute for censored linear regression by the 1-norm. We derive rates of convergence and establish asymptotic normality of the estimator of the regression coefficients. Our estimator has the same asymptotic variance as Stute's estimator in the censored linear model without outliers. Hence, there is no loss of efficiency as a result of robustness. Tests and confidence sets can therefore rely on the theory developed by Stute. The outlined procedure is also computationally advantageous, since it amounts to solving a convex optimization program. We also propose a second estimator which uses the proposed penalized Stute estimator as a first step to detect outliers. It has similar theoretical properties but better performance in finite samples as assessed by simulations. We apply the outlined procedures on data from the Ohio State transplant center.

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Inference robust to outliers with ℓ₁-norm penalization

Cited by 4 publications

References 35 publications

Robust censored regression with l1-norm regularization

Robust censored regression with l1-norm regularization

High-dimensional inference robust to outliers with l1-norm penalization

Robust censored regression with $$\ell _1$$-norm regularization

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Inference robust to outliers with ℓ1-norm penalization

Cited by 4 publications

References 35 publications

Robust censored regression with l1-norm regularization

Robust censored regression with l1-norm regularization

High-dimensional inference robust to outliers with l1-norm penalization

Robust censored regression with $$\ell _1$$-norm regularization

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Inference robust to outliers with ℓ₁-norm penalization