Independence index sufficient variable screening for categorical responses

Yuan, Qingcong; Chen, Xianyan; Ke, Chenlu; Yin, Xiangrong

doi:10.1016/j.csda.2022.107530

Cited by 4 publications

(10 citation statements)

References 34 publications

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“…As the statement of Yuan et al (2022), the analysis of sufficient variable screening includes the iterative two-step screening procedure, which contains complex computation [ 24 ]. This section will propose a novel sufficient variable screening statistic by the quantile-adaptive correlation test (QA-SVS).…”

Section: Sufficient Screening Utilitymentioning

confidence: 99%

“…The complete observations

are independent and identically distributed observation samples of

. Based on the research of Yin and Hilafu (2015) [ 23 ] and Yuan et al (2022) [ 24 ], define two indicant sets, i.e, sufficient active or active variables index set

consists of variables that are relevant to Y , and

contains all redundant predictors or noise predictors, where

is a subset of

, and

denotes the orthogonal complement of

. Sufficient variable screening means to find the smallest and unique active variable set

such that

, that is, given the set

, Y is independent of

.…”

Section: Sufficient Screening Utilitymentioning

confidence: 99%

“…Lemma 1 will be proved in Appendix A.2 . According to Yuan et al (2022) [ 24 ], the sufficient active variable set is actually screened based on the structure of

. Lemma 1 provides the information that the structure of

could be transformed into another structure based on the marginal structure of

by judging the difference of

and

for each

and

.…”

Section: Sufficient Screening Utilitymentioning

confidence: 99%

“…However, most of the above sure screening methods are not sufficient variable screening (SVS) technology, which was first proposed in Cook (2004) and also discussed by Yin and Hilafu (2015) and Yuan et al (2022) [ 22 , 23 , 24 ]. For illustration, consider a population with a response variable Y and a p -dimensional vector of predictors

, let

be a subset of

, and

denotes the orthogonal complement of

.…”

Section: Introductionmentioning

confidence: 99%

“…For illustration, consider a population with a response variable Y and a p -dimensional vector of predictors

, let

be a subset of

, and

denotes the orthogonal complement of

. Based on the research of Yin and Hilafu (2015) and Yuan et al (2022), sufficient variable screening means to find the smallest and unique active variable set

such that

, that is, given the set

, Y is independent of

[ 23 , 24 ].…”

Section: Introductionmentioning

confidence: 99%

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Quantile-Adaptive Sufficient Variable Screening by Controlling False Discovery

Yuan

Chen

Qiu

et al. 2023

Entropy

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Sufficient variable screening rapidly reduces dimensionality with high probability in ultra-high dimensional modeling. To rapidly screen out the null predictors, a quantile-adaptive sufficient variable screening framework is developed by controlling the false discovery. Without any specification of an actual model, we first introduce a compound testing procedure based on the conditionally imputing marginal rank correlation at different quantile levels of response to select active predictors in high dimensionality. The testing statistic can capture sufficient dependence through two paths: one is to control false discovery adaptively and the other is to control the false discovery rate by giving a prespecified threshold. It is computationally efficient and easy to implement. We establish the theoretical properties under mild conditions. Numerical studies including simulation studies and real data analysis contain supporting evidence that the proposal performs reasonably well in practical settings.

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Section: Sufficient Screening Utilitymentioning

confidence: 99%

“…The complete observations

are independent and identically distributed observation samples of

. Based on the research of Yin and Hilafu (2015) [ 23 ] and Yuan et al (2022) [ 24 ], define two indicant sets, i.e, sufficient active or active variables index set

consists of variables that are relevant to Y , and

contains all redundant predictors or noise predictors, where

is a subset of

, and

denotes the orthogonal complement of

. Sufficient variable screening means to find the smallest and unique active variable set

such that

, that is, given the set

, Y is independent of

.…”

Section: Sufficient Screening Utilitymentioning

confidence: 99%

“…Lemma 1 will be proved in Appendix A.2 . According to Yuan et al (2022) [ 24 ], the sufficient active variable set is actually screened based on the structure of

. Lemma 1 provides the information that the structure of

could be transformed into another structure based on the marginal structure of

by judging the difference of

and

for each

and

.…”

Section: Sufficient Screening Utilitymentioning

confidence: 99%

, let

be a subset of

, and

denotes the orthogonal complement of

.…”

Section: Introductionmentioning

confidence: 99%

“…For illustration, consider a population with a response variable Y and a p -dimensional vector of predictors

, let

be a subset of

, and

denotes the orthogonal complement of

. Based on the research of Yin and Hilafu (2015) and Yuan et al (2022), sufficient variable screening means to find the smallest and unique active variable set

such that

, that is, given the set

, Y is independent of

[ 23 , 24 ].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantile-Adaptive Sufficient Variable Screening by Controlling False Discovery

Yuan

Chen

Qiu

et al. 2023

Entropy

View full text Add to dashboard Cite

show abstract

Quantile Correlation‐Based Sufficient Variable Screening by Controlling False Discovery Rate

Qiu,

Chen,

Yuan

2024

Advcd Theory and Sims

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Sufficient variable screening (SVS) with the false discovery rate (FDR) controlled rapidly reduces dimensionality with high probability in high dimensional modeling. By using quantiles, this paper proposes a new SVS procedure by controlling the FDR based on two‐stage Pearson's goodness testing with Chi‐square statistics for high dimensional data, abbreviated as QC‐SVS‐FDR. Without any specified distribution of the actual model, the QC‐SVS‐FDR method screens important predictors by a series of testing procedures combined with the adaptive composite of Pearson's chi‐square statistics. The quantile correlation‐based sufficient utility is sensitive to capture the subtle correlations under different quantile levels and is easy to implement with computational efficiency. Asymptotic results and sufficient screening properties of the proposed methods are obtained under mild conditions. Numerical studies including simulation studies and real data analysis demonstrate the advantages of the proposed method in practical settings.

show abstract

Partial sufficient variable screening with categorical controls

Wei

Yuan

et al. 2023

Computational Statistics & Data Analysis

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Independence index sufficient variable screening for categorical responses

Cited by 4 publications

References 34 publications

Quantile-Adaptive Sufficient Variable Screening by Controlling False Discovery

Quantile-Adaptive Sufficient Variable Screening by Controlling False Discovery

Quantile Correlation‐Based Sufficient Variable Screening by Controlling False Discovery Rate

Partial sufficient variable screening with categorical controls

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