Goodness-of-fit tests for high-dimensional Gaussian linear models

DOI10.1214/08-AOS629zbMath1183.62074arXiv0711.2119OpenAlexW2075010327MaRDI QIDQ2380086

Nicolas Verzelen, Fanny Villers

Publication date: 24 March 2010

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2119

zbMATH Keywords

ellipsoidgoodness-of-fitlinear regressionmultiple testingGaussian graphical modelsadaptive testingminimax hypothesis testingminimax separation rate

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Linear regression; mixed models (62J05) Hypothesis testing in multivariate analysis (62H15) Measures of association (correlation, canonical correlation, etc.) (62H20) Applications of graph theory (05C90)

Related Items (15)

High-dimensional asymptotics of likelihood ratio tests in the Gaussian sequence model under convex constraints ⋮ Minimax adaptive tests for the functional linear model ⋮ Goodness-of-fit testing-based selection for large-\(p\)-small-\(n\) problems: a two-stage ranking approach ⋮ Goodness‐of‐fit tests for the multivariate Student‐t distribution based on i.i.d. data, and for GARCH observations ⋮ Minimax risks for sparse regressions: ultra-high dimensional phenomenons ⋮ Detection boundary in sparse regression ⋮ Combinatorial inference for graphical models ⋮ Adaptive estimation of high-dimensional signal-to-noise ratios ⋮ Optimal estimation of variance in nonparametric regression with random design ⋮ Tests for Gaussian graphical models ⋮ A global homogeneity test for high-dimensional linear regression ⋮ Optimal sparsity testing in linear regression model ⋮ Classical testing in functional linear models ⋮ A joint test for parametric specification and independence in nonlinear regression models ⋮ Detecting positive correlations in a multivariate sample

Uses Software

• GMRFLib

Cites Work

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