scholarly journals Tuning parameter selection in high dimensional penalized likelihood

2012 ◽  
Vol 75 (3) ◽  
pp. 531-552 ◽  
Author(s):  
Yingying Fan ◽  
Cheng Yong Tang
Keyword(s):  
Penalized Likelihood ◽  
Parameter Selection ◽  
Tuning Parameter ◽  
High Dimensional

scholarly journals A Survey of Tuning Parameter Selection for High-Dimensional Regression

2020 ◽  
Vol 7 (1) ◽  
pp. 209-226 ◽  
Author(s):  
Yunan Wu ◽  
Lan Wang
Keyword(s):  
Standard Technique ◽  
Penalized Regression ◽  
Optimal Choice ◽  
Parameter Selection ◽  
Tuning Parameter ◽  
High Dimensional ◽  
Design Matrix ◽  
High Dimensional Regression ◽  
Selection For ◽  
Sparsity Level

Penalized (or regularized) regression, as represented by lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of penalized regression relies crucially on the choice of the tuning parameter, which determines the amount of regularization and hence the sparsity level of the fitted model. The optimal choice of tuning parameter depends on both the structure of the design matrix and the unknown random error distribution (variance, tail behavior, etc.). This article reviews the current literature of tuning parameter selection for high-dimensional regression from both the theoretical and practical perspectives. We discuss various strategies that choose the tuning parameter to achieve prediction accuracy or support recovery. We also review several recently proposed methods for tuning-free high-dimensional regression.

scholarly journals On the Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study

2019 ◽  
Author(s):  
Hui Xiao ◽  
Yiguo Sun
Keyword(s):  
Monte Carlo ◽  
Model Selection ◽  
Sample Size ◽  
Model Averaging ◽  
Parameter Selection ◽  
Tuning Parameter ◽  
High Dimensional ◽  
Finite Sample ◽  
Sparse Models ◽  
Mallows Model

Model selection and model averaging have been the popular approaches in handling modelling uncertainties. Fan and Li(2006) laid out a unified frame work for variable selection via penalized likelihood. The tuning parameter selection is vital in the optimization problem for the penalized estimators in achieving consistent selection and optimal estimation. Since the OLSpost-LASSO estimator by Belloni and Chernozhukov (2013), few studies have focused on the finite sample performances of the class of OLS post-penalty estimators with the tuning parameter choice determined by different tuning parameter selection approaches. We aim to supplement the existing model selection literature by studying such a class of OLS post-selection estimators. Inspired by the Shrinkage Averaging Estimator (SAE) by Schomaker(2012) and the Mallows Model Averaging (MMA) criterion by Hansen (2007), we further propose a Shrinkage Mallows Model Averaging (SMMA) estimator for averaging high dimensional sparse models. Based on the Monte Carlo design by Wang et al. (2009) which features an expanding sparse parameter space as the sample size increases, our Monte Carlo design further considers the effect of the effective sample size and the degree of model sparsity on the finite sample performances of model selection and model averaging estimators. From our data examples, we find that the OLS post-SCAD(BIC) estimator in finite sample outperforms most of the current penalized least squares estimators as long as the number of parameters does not exceed the sample size. In addition, the SMMA performs better given sparser models. This supports the use of the SMMA estimator when averaging high dimensional sparse models.

scholarly journals On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study

2019 ◽  
Vol 12 (3) ◽  
pp. 109 ◽  
Author(s):  
Hui Xiao ◽  
Yiguo Sun
Keyword(s):  
Monte Carlo ◽  
Model Selection ◽  
Model Averaging ◽  
Ordinary Least Squares ◽  
Parameter Selection ◽  
Tuning Parameter ◽  
High Dimensional ◽  
Finite Sample ◽  
Sparse Models ◽  
Modeling Uncertainties

Model selection and model averaging are popular approaches for handling modeling uncertainties. The existing literature offers a unified framework for variable selection via penalized likelihood and the tuning parameter selection is vital for consistent selection and optimal estimation. Few studies have explored the finite sample performances of the class of ordinary least squares (OLS) post-selection estimators with the tuning parameter determined by different selection approaches. We aim to supplement the literature by studying the class of OLS post-selection estimators. Inspired by the shrinkage averaging estimator (SAE) and the Mallows model averaging (MMA) estimator, we further propose a shrinkage MMA (SMMA) estimator for averaging high-dimensional sparse models. Our Monte Carlo design features an expanding sparse parameter space and further considers the effect of the effective sample size and the degree of model sparsity on the finite sample performances of estimators. We find that the OLS post-smoothly clipped absolute deviation (SCAD) estimator with the tuning parameter selected by the Bayesian information criterion (BIC) in finite sample outperforms most penalized estimators and that the SMMA performs better when averaging high-dimensional sparse models.

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