Consistent variable selection in high dimensional regression via multiple testing

2006 ◽  
Vol 136 (12) ◽  
pp. 4349-4364 ◽  
Author(s):  
Florentina Bunea ◽  
Marten H. Wegkamp ◽  
Anna Auguste
Keyword(s):  
Variable Selection ◽  
Multiple Testing ◽  
High Dimensional ◽  
High Dimensional Regression

scholarly journals A One-Covariate at a Time, Multiple Testing Approach to Variable Selection in High-Dimensional Linear Regression Models

2016 ◽  
Vol 2016 (290) ◽  
Author(s):  
Alexander Chudik ◽  
◽  
George Kapetanios ◽  
M. Hashem Pesaran ◽  
◽  
...  
Keyword(s):  
Linear Regression ◽  
Variable Selection ◽  
Regression Models ◽  
Multiple Testing ◽  
High Dimensional ◽  
Linear Regression Models ◽  
Testing Approach

Consistent significance controlled variable selection in high-dimensional regression

Stat ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. e210 ◽  
Author(s):  
Adriano Zanin Zambom ◽  
Jongwook Kim
Keyword(s):  
Variable Selection ◽  
High Dimensional ◽  
High Dimensional Regression

scholarly journals High-dimensional regression in practice: an empirical study of finite-sample prediction, variable selection and ranking

2019 ◽  
Vol 30 (3) ◽  
pp. 697-719 ◽  
Author(s):  
Fan Wang ◽  
Sach Mukherjee ◽  
Sylvia Richardson ◽  
Steven M. Hill
Keyword(s):  
Variable Selection ◽  
Large Scale ◽  
Penalized Regression ◽  
Adaptive Lasso ◽  
High Dimensional ◽  
Finite Sample ◽  
Dantzig Selector ◽  
Regression Methods ◽  
High Dimensional Regression ◽  
Selection And Ranking

AbstractPenalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well developed, the relative efficacy of different approaches in finite-sample settings, as encountered in practice, remains incompletely understood. There is therefore a need for empirical investigations in this area that can offer practical insight and guidance to users. In this paper, we present a large-scale comparison of penalized regression methods. We distinguish between three related goals: prediction, variable selection and variable ranking. Our results span more than 2300 data-generating scenarios, including both synthetic and semisynthetic data (real covariates and simulated responses), allowing us to systematically consider the influence of various factors (sample size, dimensionality, sparsity, signal strength and multicollinearity). We consider several widely used approaches (Lasso, Adaptive Lasso, Elastic Net, Ridge Regression, SCAD, the Dantzig Selector and Stability Selection). We find considerable variation in performance between methods. Our results support a “no panacea” view, with no unambiguous winner across all scenarios or goals, even in this restricted setting where all data align well with the assumptions underlying the methods. The study allows us to make some recommendations as to which approaches may be most (or least) suitable given the goal and some data characteristics. Our empirical results complement existing theory and provide a resource to compare methods across a range of scenarios and metrics.

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