Oracle inequalities for cross-validation type procedures

DOI10.1214/12-EJS730zbMath1295.62051MaRDI QIDQ1950881

Charles Mitchell, Guillaume Lecué

Publication date: 28 May 2013

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

Full work available at URL: https://projecteuclid.org/euclid.ejs/1349355603

zbMATH Keywords

aggregationcross-validationadaptationsparsity

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Nonparametric hypothesis testing (62G10) Ridge regression; shrinkage estimators (Lasso) (62J07) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Nonparametric tolerance and confidence regions (62G15) Statistical ranking and selection procedures (62F07)

Related Items (5)

On cross-validated Lasso in high dimensions ⋮ A Cross-Validated Ensemble Approach to Robust Hypothesis Testing of Continuous Nonlinear Interactions: Application to Nutrition-Environment Studies ⋮ Aggregated hold out for sparse linear regression with a robust loss function ⋮ Localization of VC classes: beyond local Rademacher complexities ⋮ Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases

Uses Software

• glmnet

Cites Work

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• Statistics for high-dimensional data. Methods, theory and applications.
• Aggregation via empirical risk minimization
• Concentration inequalities and model selection. Ecole d'Eté de Probabilités de Saint-Flour XXXIII -- 2003.
• A survey of cross-validation procedures for model selection
• A tail inequality for suprema of unbounded empirical processes with applications to Markov chains
• Large sample optimality of least squares cross-validation in density estimation
• An asymptotically optimal window selection rule for kernel density estimates
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• Estimation of dependences based on empirical data. Transl. from the Russian by Samuel Kotz
• Risk bounds for model selection via penalization
• Smooth discrimination analysis
• Mixing strategies for density estimation.
• Statistical learning theory and stochastic optimization. Ecole d'Eté de Probabilitiés de Saint-Flour XXXI -- 2001.
• Statistical behavior and consistency of classification methods based on convex risk minimization.
• Optimal aggregation of classifiers in statistical learning.
• Weak convergence and empirical processes. With applications to statistics
• Local Rademacher complexities and oracle inequalities in risk minimization. (2004 IMS Medallion Lecture). (With discussions and rejoinder)
• Optimal rates and adaptation in the single-index model using aggregation
• Optimal rates of aggregation in classification under low noise assumption
• Empirical minimization
• Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates
• Oracle inequalities for multi-fold cross validation
• Distribution-free performance bounds for potential function rules
• Uniform Central Limit Theorems
• The Generic Chaining
• 10.1162/153244302760200704
• Linear Model Selection by Cross-Validation
• Regularization and Variable Selection Via the Elastic Net
• Suboptimality of Penalized Empirical Risk Minimization in Classification
• Convexity, Classification, and Risk Bounds

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