A systematic review on model selection in high-dimensional regression

DOI10.1016/j.jkss.2018.10.001zbMath1411.62204OpenAlexW2900489223WikidataQ128948583 ScholiaQ128948583MaRDI QIDQ1726155

Jinwoo Cho, Kyusang Yu, Eun Ryung Lee

Publication date: 19 February 2019

Published in: Journal of the Korean Statistical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jkss.2018.10.001

zbMATH Keywords

model selectionquantile regressionlinear regressionoracle propertyLassoSCADpenalized methodsmodel selection consistencygeneral convex losshigh dimensional regression modelshigh level conditionsquadratic margin condition

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Ridge regression; shrinkage estimators (Lasso) (62J07) Linear regression; mixed models (62J05)

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Regularization statistical inferences for partially linear models with high dimensional endogenous covariates ⋮ Modified Mahalanobis-Taguchi system based on proper orthogonal decomposition for high-dimensional-small-sample-size data classification ⋮ Penalized kernel quantile regression for varying coefficient models

Cites Work

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• Nearly unbiased variable selection under minimax concave penalty
• The Adaptive Lasso and Its Oracle Properties
• Statistics for high-dimensional data. Methods, theory and applications.
• One-step sparse estimates in nonconcave penalized likelihood models
• Nonconcave penalized likelihood with a diverging number of parameters.
• On the conditions used to prove oracle results for the Lasso
• Simultaneous analysis of Lasso and Dantzig selector
• High-dimensional generalized linear models and the lasso
• Calibrating nonconvex penalized regression in ultra-high dimension
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Square root penalty: Adaption to the margin in classification and in edge estimation
• Extended BIC for small-n-large-P sparse GLM
• Large sample properties of the smoothly clipped absolute deviation penalized maximum likelihood estimation on high dimensions
• Global optimality of nonconvex penalized estimators
• Shrinkage Tuning Parameter Selection with a Diverging number of Parameters
• Extended Bayesian information criteria for model selection with large model spaces
• A Selective Overview of Variable Selection in High Dimensional Feature Space (Invited Review Article)
• Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
• Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension
• Model Selection via Bayesian Information Criterion for Quantile Regression Models
• Regularization Parameter Selections via Generalized Information Criterion
• Smoothly Clipped Absolute Deviation on High Dimensions
• Tuning parameter selectors for the smoothly clipped absolute deviation method