Variable selection and parameter estimation for partially linear models via Dantzig selector

Li, Feng; Lin, Lu; Su, Yuxia

doi:10.1007/s00184-012-0384-x

Cited by 3 publications

(13 citation statements)

References 32 publications

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“…Recently Li et al. 28 show that the Dantzig selector might not be consistent. The adaptive Dantzig selector and its consistency for censored data are also discussed in Bickel et al.…”

Section: Methodsmentioning

confidence: 99%

“…The details of basic weighted Dantzig selector are given in Li et al. 28 The adaptive Dantzig selector estimator is the solution to where w is the data-dependent weights vector and Y^(β^ini) are the imputed failure times obtained using equation (4).…”

Section: Methodsmentioning

confidence: 99%

“…Recently, Lin et al. 28 and Johnson et al. 27 also studied Buckley–James estimation using the Dantzig selector with an initial n-consistent estimator.…”

Section: Introductionmentioning

confidence: 99%

“…To deal with the high-dimensional problem, Lin et al. 28 used the procedure of Zhu et al. 33 to select the subset of important covariates.…”

Section: Introductionmentioning

confidence: 99%

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Variable selection for accelerated lifetime models with synthesized estimation techniques

Khan

Shaw

2017

Stat Methods Med Res

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We develop variable selection approaches for accelerated failure time models, consisting of a group of algorithms based on a synthesis of two widely used techniques in the area of variable selection for survival analysis-the Buckley-James method and the Dantzig selector. Two algorithms are based on proposed modified Buckley-James estimating methods that are designed for high-dimensional censored data. Another two algorithms are based on a two-stage weighted Dantzig selector method where weights are obtained from the two proposed synthesis-based algorithms. The methods are easy to understand and they perform estimation and variable selection simultaneously. Furthermore, they can deal with collinearity among the covariates. We conducted several simulation studies and one empirical analysis with a microarray dataset; these studies demonstrated satisfactory variable selection performance. In addition, the microarray data analysis shows the methods performing similarly to three other correlation-based greedy variable selection techniques in the literature-sure independence screening, tilted correlation screening (TCS), and partial correlation (PC) simple. This empirical study also found that the sure independence screening technique considerably improves the performance of most of the proposed methods.

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“…Recently Li et al. 28 show that the Dantzig selector might not be consistent. The adaptive Dantzig selector and its consistency for censored data are also discussed in Bickel et al.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…Recently, Lin et al. 28 and Johnson et al. 27 also studied Buckley–James estimation using the Dantzig selector with an initial n-consistent estimator.…”

Section: Introductionmentioning

confidence: 99%

“…To deal with the high-dimensional problem, Lin et al. 28 used the procedure of Zhu et al. 33 to select the subset of important covariates.…”

Section: Introductionmentioning

confidence: 99%

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Variable selection for accelerated lifetime models with synthesized estimation techniques

Khan

Shaw

2017

Stat Methods Med Res

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“…31 In Ref. 32, the Dantzig selector (DS) [33][34][35] is applied to estimate new additions by transforming the selection of the best subset of variables into the solving of a very simple convex program, which, in fact, can easily be recast as a convenient linear program (LP). However, solving the linear programming problem requires a high computational complexity, 36 which is greatly limiting its practical application.…”

Section: Introductionmentioning

confidence: 99%

Exploiting time varying sparsity for underwater acoustic communication via dynamic compressed sensing

Jiang

Zheng

Zhou

et al. 2018

The Journal of the Acoustical Society of America

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While it has been recognized that the multipath structure of the underwater acoustic (UWA) channel offers the potential for compressed sensing (CS) sparsity exploitation, the rapidly time varying arrivals induced by highly dynamic surfaces unfortunately pose significant difficulties to channel estimation. From the viewpoint of underwater acoustic propagation, with the exception of the highly time varying arrivals caused by dynamic surface, generally there exist relatively stationary or slowly changing arrivals caused by direct path or bottom reflection, which imply the adoption of a discriminate estimation method to handle sparse components with different time variation scale. By modeling the time varying UWA channels as a sparse set consisting of constant and timevarying supports, in this paper, estimation of time varying UWA channel is transformed into a problem of dynamic compressed sensing sparse recovery. The combination of a Kalman filter and compressed sensing is adopted to pursue the solution of it. Numerical simulations demonstrate the superiority of the proposed algorithm. In the form of a channel-estimation-based decision-feedback equalizer, the experimental results with the field data obtained in a shallow water acoustic communication experiment indicate that the proposed dynamic compressed sensing algorithm outperforms classic algorithms as well as CS algorithms.

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Variable selection for censored data using Modified Correlation Adjusted coRrelation (MCAR) scores

Mimi

Khan

2021

Statistics in Medicine

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Dealing with high-dimensional censored data is very challenging because of the complexities in data structure. This article focuses on developing a variable selection procedure for censored high-dimensional data with the AFT models using the Modified Correlation Adjusted coRrelation (MCAR) scores method.The latter is developed based on CAR scores method that provides a canonical ordering that encourages grouping of correlated predictors and down-weights antagonistic variables. The proposed MCAR scores method is developed as an extension of the CAR scores method using NOVEL integration of the sample and threshold estimator of the correlation matrix as suggested by Huang and Frylewicz. The proposed MCAR exhibits computationally more efficient estimates under model sparsity and can provide a canonical ordering among the predictors. The MCAR method is a greedy method that is also easy to understand and can perform estimation and variable selection simultaneously.Performances of variable selection by the MCAR method have been compared with other existing regularized techniques in literature-such as the lasso, elastic net and with a machine learning technique called boosting and with the censored CAR by a number of simulation studies and a real microarray data set called diffuse large-B-cell lymphoma. Results indicate that when correlation exists among the covariates, the MCAR method outperforms all five techniques while for uncorrelated data, the MCAR performs quite similar to the CAR method but clearly outperforms the other three methods. The empirical study further reveals that the MCAR method exhibits the best predictive performance among the methods.

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Variable selection and parameter estimation for partially linear models via Dantzig selector

Cited by 3 publications

References 32 publications

Variable selection for accelerated lifetime models with synthesized estimation techniques

Variable selection for accelerated lifetime models with synthesized estimation techniques

Exploiting time varying sparsity for underwater acoustic communication via dynamic compressed sensing

Variable selection for censored data using Modified Correlation Adjusted coRrelation (MCAR) scores

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