Conditional sure independence screening by conditional marginal empirical likelihood

Hu, Qinqin; Lin, Lu

doi:10.1007/s10463-015-0534-9

Cited by 15 publications

(5 citation statements)

References 35 publications

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“…To simplify the notation, we use Ûi,jk = [X ij − E(X j |x iC )]Y ik . Similar to the proof of Lemma 4 inHu and Lin (2017) and using the similar technique in the proof of Lemma 4.1, we can prove that P{ l c j (0) < 2t} ≤ P…”

mentioning

confidence: 71%

“…To avoid such a risk, statisticians developed the model-free methods, some typical works include but are not limited to Li et al (2012), Cui et al (2015), Lu and Lin (2017), Pan et al (2019) and the reference therein. Additionally, to reduce the negative effect caused by the complicated correlation among predictors, researchers also put forward some conditional screening methods, see Barut et al (2015), Hu and Lin (2017), Lin and Sun (2016) and Lu and Lin (2017).…”

Section: Introductionmentioning

confidence: 99%

“…Due to the nice property of empirical likelihood, ELSIS is able to incorporate additionally the level of uncertainties associated with estimators and adapts to the heterogeneity in the conditional variance of random error. Motivated by the work of Chang et al (2013a), Hu and Lin (2017) generalized the ELSIS method to a conditional version.…”

Section: Introductionmentioning

confidence: 99%

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Feature screening for multi-response linear models by empirical likelihood

Azhari¹,

Li²

2022

Preprint

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This paper proposes a new feature screening method for the multi-response ultrahigh dimensional linear model by empirical likelihood. Through a multivariate moment condition, the empirical likelihood induced ranking statistics can exploit the joint effect among responses, and thus result in a much better performance than the methods considering responses individually. More importantly, by the use of empirical likelihood, the new method adapts to the heterogeneity in the conditional variance of random error. The sure screening property of the newly proposed method is proved with the model size controlled within a reasonable scale. Additionally, the new screening method is also extended to a conditional version so that it can recover the hidden predictors which are easily missed by the unconditional method. The corresponding theoretical properties are also provided. Finally, both numerical studies and real data analysis are provided to illustrate the effectiveness of the proposed methods.

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mentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

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Feature screening for multi-response linear models by empirical likelihood

Azhari¹,

Li²

2022

Preprint

Self Cite

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show abstract

“…The empirical likelihood method usually can improve the confidence region, can increase the accuracy of coverage, can be implemented easily, and can be studentized automatically. There have been many literary works that discuss the empirical likelihood method and its applications, for example, An and Zhao (); Cui, Guo, Lin, and Zhu (); Hu and Lin (); Kiwitt and Neumeyer (); Lian (); and Liu and Xia ().…”

Section: Estimation Methodologymentioning

confidence: 99%

Nonlinear regression models with single‐index heteroscedasticity

Zhang

Gai

Lin

et al. 2019

Statistica Neerlandica

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We consider nonlinear heteroscedastic single‐index models where the mean function is a parametric nonlinear model and the variance function depends on a single‐index structure. We develop an efficient estimation method for the parameters in the mean function by using the weighted least squares estimation, and we propose a “delete‐one‐component” estimator for the single‐index in the variance function based on absolute residuals. Asymptotic results of estimators are also investigated. The estimation methods for the error distribution based on the classical empirical distribution function and an empirical likelihood method are discussed. The empirical likelihood method allows for incorporation of the assumptions on the error distribution into the estimation. Simulations illustrate the results, and a real chemical data set is analyzed to demonstrate the performance of the proposed estimators.

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“…Since then, conditional screening method has drawn much interest and various conditional screening approaches have been proposed under different scenarios. For example, Hu and Lin (2017), Liu and Wang (2018), and Lu and Lin (2020) developed different conditional screening procedures for ultrahigh-dimensional complete data, Liu and Chen (2018) considered the conditional quantile independence screening approach for ultrahigh-dimensional heterogeneous data, and Hong et al (2018) developed a conditional screening method for censored survival data under the proportional hazards model. Simulation studies demonstrated that these conditional screening approaches can provide a powerful means to identify hidden active variables for ultrahigh-dimensional data.…”

Section: Introductionmentioning

confidence: 99%

Model‐free conditional screening for ultrahigh‐dimensional survival data via conditional distance correlation

et al. 2022

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How to select the active variables that have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh‐dimensional data. In many applications, researchers often know that a certain set of covariates are active variables from some previous investigations and experiences. With the knowledge of the important prior knowledge of active variables, we propose a model‐free conditional screening procedure for ultrahigh dimensional survival data based on conditional distance correlation. The proposed procedure can effectively detect the hidden active variables that are jointly important but are weakly correlated with the response. Moreover, it performs well when covariates are strongly correlated with each other. We establish the sure screening property and the ranking consistency of the proposed method and conduct extensive simulation studies, which suggests that the proposed procedure works well for practical situations. Then, we illustrate the new approach through a real dataset from the diffuse large‐B‐cell lymphoma study S1.

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Conditional sure independence screening by conditional marginal empirical likelihood

Cited by 15 publications

References 35 publications

Feature screening for multi-response linear models by empirical likelihood

Feature screening for multi-response linear models by empirical likelihood

Nonlinear regression models with single‐index heteroscedasticity

Model‐free conditional screening for ultrahigh‐dimensional survival data via conditional distance correlation

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