Confidence sets based on penalized maximum likelihood estimators in Gaussian regression

DOI10.1214/09-EJS523zbMath1329.62156arXiv0806.1652OpenAlexW2041584646MaRDI QIDQ1952055

Ulrike Schneider, Benedikt M. Pötscher

Publication date: 27 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.1652

zbMATH Keywords

model selectioncoverage probabilitysparsityconfidence setLassoadaptive Lassohard-thresholdingpenalized least squarespenalized maximum likelihoodsoft-thresholding

Mathematics Subject Classification ID

Parametric tolerance and confidence regions (62F25) Ridge regression; shrinkage estimators (Lasso) (62J07)

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Cites Work

• Unnamed Item
• The Adaptive Lasso and Its Oracle Properties
• Sparse estimators and the oracle property, or the return of Hodges' estimator
• On the distribution of penalized maximum likelihood estimators: the LASSO, SCAD, and thresholding
• Confidence sets based on sparse estimators are necessarily large
• On the distribution of the adaptive LASSO estimator
• Asymptotics for Lasso-type estimators.
• A Lemma on Stochastic Majorization and Properties of the Student Distribution
• Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
• A Statistical View of Some Chemometrics Regression Tools
• Admissibility of the Usual Confidence Sets for the Mean of a Univariate or Bivariate Normal Population