A new perspective on robust \(M\)-estimation: finite sample theory and applications to dependence-adjusted multiple testing

DOI10.1214/17-AOS1606zbMath1409.62154arXiv1711.05381OpenAlexW3106083453WikidataQ58767782 ScholiaQ58767782MaRDI QIDQ1800789

Han Liu, Koushiki Bose, Wen-Xin Zhou, Jianqing Fan

Publication date: 24 October 2018

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

Full work available at URL: https://arxiv.org/abs/1711.05381

zbMATH Keywords

Bahadur representation\(M\)-estimatorfalse discovery proportionlarge-scale multiple testingheavy-tailed dataapproximate factor modelHuber loss

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Linear regression; mixed models (62J05) Hypothesis testing in multivariate analysis (62H15) Robustness and adaptive procedures (parametric inference) (62F35) Paired and multiple comparisons; multiple testing (62J15)

Related Items

A New Principle for Tuning-Free Huber Regression, Refined Cramér-type moderate deviation theorems for general self-normalized sums with applications to dependent random variables and winsorized mean, FarmTest: Factor-Adjusted Robust Multiple Testing With Approximate False Discovery Control, The robust nearest shrunken centroids classifier for high-dimensional heavy-tailed data, Concentration study of M-estimators using the influence function, Robust post-selection inference of high-dimensional mean regression with heavy-tailed asymmetric or heteroskedastic errors, Robust statistical learning with Lipschitz and convex loss functions, Distributed Sparse Composite Quantile Regression in Ultrahigh Dimensions, Huber estimation for the network autoregressive model, Robust distributed multicategory angle-based classification for massive data, Unnamed Item, Robust matrix estimations meet Frank-Wolfe algorithm, Robust inference for high‐dimensional single index models, Robust inference via multiplier bootstrap, Robust high-dimensional tuning free multiple testing, Robust Signal Recovery for High-Dimensional Linear Log-Contrast Models with Compositional Covariates, Renewable Huber estimation method for streaming datasets, Robust projected principal component analysis for large-dimensional semiparametric factor modeling, Nonasymptotic analysis of robust regression with modified Huber's loss, A multiple testing approach to the regularisation of large sample correlation matrices, A MOM-based ensemble method for robustness, subsampling and hyperparameter tuning, Matrix optimization based Euclidean embedding with outliers, Distributed adaptive Huber regression, Quantile regression feature selection and estimation with grouped variables using Huber approximation, Unnamed Item, Functional linear regression with Huber loss

Uses Software

• FAMT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
• Robust estimation of \(U\)-statistics
• Cramér-type moderate deviations for Studentized two-sample \(U\)-statistics with applications
• Phase transition and regularized bootstrap in large-scale \(t\)-tests with false discovery rate control
• Bootstrap confidence sets under model misspecification
• Cramér-type moderate deviation for the maximum of the periodogram with application to simultaneous tests in gene expression time series
• Robustness of multiple testing procedures against dependence
• Asymptotic behavior of M estimators of p regression parameters when \(p^ 2/n\) is large. II: Normal approximation
• Asymptotics with increasing dimension for robust regression with applications to the bootstrap
• Asymptotic behavior of M-estimators for the linear model
• The weighted bootstrap
• A general Bahadur representation of \(M\)-estimators and its application to linear regression with nonstochastic designs
• On parameters of increasing dimensions
• Robust regression: Asymptotics, conjectures and Monte Carlo
• The control of the false discovery rate in multiple testing under dependency.
• A stochastic process approach to false discovery control.
• Challenging the empirical mean and empirical variance: a deviation study
• Marginal asymptotics for the ``large \(p\), small \(n\) paradigm: with applications to microarray data
• Generalizations of the familywise error rate
• Eigenvalue Ratio Test for the Number of Factors
• Large-Scale Multiple Testing under Dependence
• A general framework for multiple testing dependence
• A Factor Model Approach to Multiple Testing Under Dependence
• The effect of correlation in false discovery rate estimation
• To How Many Simultaneous Hypothesis Tests Can Normal, Student'stor Bootstrap Calibration Be Applied?
• Empirical Bayes Analysis of a Microarray Experiment
• Robustness and Accuracy of Methods for High Dimensional Data Analysis Based on Student’s t-Statistic
• Empirical properties of asset returns: stylized facts and statistical issues
• Estimating False Discovery Proportion Under Arbitrary Covariance Dependence
• Strong Control, Conservative Point Estimation and Simultaneous Conservative Consistency of False Discovery Rates: A Unified Approach
• A Direct Approach to False Discovery Rates
• Cross-Dimensional Inference of Dependent High-Dimensional Data
• Correlation and Large-Scale Simultaneous Significance Testing
• Estimation of the False Discovery Proportion with Unknown Dependence
• Estimation of High Dimensional Mean Regression in the Absence of Symmetry and Light Tail Assumptions
• Estimating the Proportion of True Null Hypotheses, with application to DNA Microarray Data
• Large-Scale Simultaneous Hypothesis Testing
• Robust Estimation of a Location Parameter