Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties

2001 ◽  
Vol 96 (456) ◽  
pp. 1348-1360 ◽  
Author(s):  
Jianqing Fan ◽  
Runze Li
Keyword(s):  
Variable Selection ◽  
Penalized Likelihood ◽  
Oracle Properties

scholarly journals A mixture of local and quadratic approximation variable selection algorithm in nonconcave penalized regression

2013 ◽  
Vol Volume 16, 2012 ◽  
Author(s):  
Assi N'GUESSAN ◽  
Ibrahim Sidi Zakari ◽  
Assi Mkhadri
Keyword(s):  
Variable Selection ◽  
Penalized Likelihood ◽  
Real Data ◽  
Penalized Regression ◽  
Penalty Functions ◽  
Selection Algorithm ◽  
Data Set ◽  
International Audience ◽  
One Step ◽  
Nonconvex Penalty

International audience We consider the problem of variable selection via penalized likelihood using nonconvex penalty functions. To maximize the non-differentiable and nonconcave objective function, an algorithm based on local linear approximation and which adopts a naturally sparse representation was recently proposed. However, although it has promising theoretical properties, it inherits some drawbacks of Lasso in high dimensional setting. To overcome these drawbacks, we propose an algorithm (MLLQA) for maximizing the penalized likelihood for a large class of nonconvex penalty functions. The convergence property of MLLQA and oracle property of one-step MLLQA estimator are established. Some simulations and application to a real data set are also presented.

Variable selection in rank regression for analyzing longitudinal data

2016 ◽  
Vol 27 (8) ◽  
pp. 2447-2458 ◽  
Author(s):  
Liya Fu ◽  
You-Gan Wang
Keyword(s):  
Variable Selection ◽  
Longitudinal Data ◽  
Adaptive Lasso ◽  
New Method ◽  
Dispersion Function ◽  
Simulation Studies ◽  
Rank Regression ◽  
Oracle Properties ◽  
Effective Selection ◽  
Selection Of

In this paper, we consider variable selection in rank regression models for longitudinal data. To obtain both robustness and effective selection of important covariates, we propose incorporating shrinkage by adaptive lasso or SCAD in the Wilcoxon dispersion function and establishing the oracle properties of the new method. The new method can be conveniently implemented with the statistical software R. The performance of the proposed method is demonstrated via simulation studies. Finally, two datasets are analyzed for illustration. Some interesting findings are reported and discussed.

scholarly journals Estimation for Varying Coefficient Models with Hierarchical Structure

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 132
Author(s):  
Feng Li ◽  
Yajie Li ◽  
Sanying Feng
Keyword(s):  
Variable Selection ◽  
Hierarchical Structure ◽  
Kernel Method ◽  
Real Data ◽  
Unknown Coefficient ◽  
Nonparametric Model ◽  
Finite Sample ◽  
Oracle Properties ◽  
Varying Coefficient ◽  
The Hierarchical Structure

The varying coefficient (VC) model is a generalization of ordinary linear model, which can not only retain strong interpretability but also has the flexibility of the nonparametric model. In this paper, we investigate a VC model with hierarchical structure. A unified variable selection method for VC model is proposed, which can simultaneously select the nonzero effects and estimate the unknown coefficient functions. Meanwhile, the selected model enforces the hierarchical structure, that is, interaction terms can be selected into the model only if the corresponding main effects are in the model. The kernel method is employed to estimate the varying coefficient functions, and a combined overlapped group Lasso regularization is introduced to implement variable selection to keep the hierarchical structure. It is proved that the proposed penalty estimators have oracle properties, that is, the coefficients are estimated as well as if the true model were known in advance. Simulation studies and a real data analysis are carried out to examine the performance of the proposed method in finite sample case.

scholarly journals Erratum to: Variable Selection in Joint Mean and Dispersion Models via Double Penalized Likelihood

Sankhya B ◽  
2014 ◽  
Vol 76 (2) ◽  
pp. 335-335
Author(s):  
Christiana Charalambous ◽  
Jianxin Pan ◽  
Mark Tranmer
Keyword(s):  
Variable Selection ◽  
Penalized Likelihood ◽  
Dispersion Models

Estimation and variable selection via frailty models with penalized likelihood

2012 ◽  
Vol 31 (20) ◽  
pp. 2223-2239 ◽  
Author(s):  
E. Androulakis ◽  
C. Koukouvinos ◽  
F. Vonta
Keyword(s):  
Variable Selection ◽  
Penalized Likelihood ◽  
Frailty Models

Variable Selection in Joint Mean and Dispersion Models via Double Penalized Likelihood

Sankhya B ◽  
2014 ◽  
Vol 76 (2) ◽  
pp. 276-304
Author(s):  
Christiana Charalambous ◽  
Jianxin Pan ◽  
Mark Tranmer
Keyword(s):  
Variable Selection ◽  
Penalized Likelihood ◽  
Dispersion Models

Efficient robust doubly adaptive regularized regression with applications

2018 ◽  
Vol 28 (7) ◽  
pp. 2210-2226 ◽  
Author(s):  
Rohana J Karunamuni ◽  
Linglong Kong ◽  
Wei Tu
Keyword(s):  
Variable Selection ◽  
Breakdown Point ◽  
Practical Implementation ◽  
Regularized Regression ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Oracle Properties ◽  
Adaptive Weights ◽  
Monte Carlo Studies ◽  
Finite Sample Breakdown Point

We consider the problem of estimation and variable selection for general linear regression models. Regularized regression procedures have been widely used for variable selection, but most existing methods perform poorly in the presence of outliers. We construct a new penalized procedure that simultaneously attains full efficiency and maximum robustness. Furthermore, the proposed procedure satisfies the oracle properties. The new procedure is designed to achieve sparse and robust solutions by imposing adaptive weights on both the decision loss and the penalty function. The proposed method of estimation and variable selection attains full efficiency when the model is correct and, at the same time, achieves maximum robustness when outliers are present. We examine the robustness properties using the finite-sample breakdown point and an influence function. We show that the proposed estimator attains the maximum breakdown point. Furthermore, there is no loss in efficiency when there are no outliers or the error distribution is normal. For practical implementation of the proposed method, we present a computational algorithm. We examine the finite-sample and robustness properties using Monte Carlo studies. Two datasets are also analyzed.

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