Are discoveries spurious? Distributions of maximum spurious correlations and their applications

DOI10.1214/17-AOS1575zbMath1402.62097arXiv1502.04237OpenAlexW178948881WikidataQ55399837 ScholiaQ55399837MaRDI QIDQ1650067

Y. Aharonov

Publication date: 29 June 2018

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

Full work available at URL: https://arxiv.org/abs/1502.04237

zbMATH Keywords

asymptotic distributionconsistencydata miningmachine learningLassoSCADhigh dimensionexogeneitymultiplier bootstrapcovariatespurious correlationfalse discoverysub-Gaussiansparse linear model

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Applications of statistics to biology and medical sciences; meta analysis (62P10) Parametric hypothesis testing (62F03) Measures of association (correlation, canonical correlation, etc.) (62H20) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (10)

Semi-Standard Partial Covariance Variable Selection When Irrepresentable Conditions Fail ⋮ Quantification of model bias underlying the phenomenon of Einstein from Noise ⋮ Testing the martingale difference hypothesis in high dimension ⋮ Bootstrapping max statistics in high dimensions: near-parametric rates under weak variance decay and application to functional and multinomial data ⋮ Inference on the best policies with many covariates ⋮ Comment on “A Tuning-Free Robust and Efficient Approach to High-Dimensional Regression” ⋮ Testing Endogeneity with High Dimensional Covariates ⋮ Largest entries of sample correlation matrices from equi-correlated normal populations ⋮ Sparse Sliced Inverse Regression Via Lasso ⋮ Asymptotic analysis for extreme eigenvalues of principal minors of random matrices

Uses Software

• ElemStatLearn

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nearly unbiased variable selection under minimax concave penalty
• Gaussian approximation of suprema of empirical processes
• Statistics for high-dimensional data. Methods, theory and applications.
• Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices
• Some nonasymptotic results on resampling in high dimension. I: Confidence regions
• One-step sparse estimates in nonconcave penalized likelihood models
• Generalized bootstrap for estimating equations
• Weak convergence and empirical processes. With applications to statistics
• Simultaneous analysis of Lasso and Dantzig selector
• Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
• Necessary and sufficient conditions for the asymptotic distributions of coherence of ultra-high dimensional random matrices
• Multiple testing procedures with applications to genomics.
• Strong oracle optimality of folded concave penalized estimation
• Endogeneity in high dimensions
• Distributions of Angles in Random Packing on Spheres
• A Selective Overview of Variable Selection in High Dimensional Feature Space (Invited Review Article)
• Testing Against a High Dimensional Alternative
• Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
• Simulation‐based hypothesis testing of high dimensional means under covariance heterogeneity
• Variance Estimation Using Refitted Cross-Validation in Ultrahigh Dimensional Regression
• Two-Sample Test of High Dimensional Means Under Dependence
• Consistent Tests for Stochastic Dominance
• Inference When a Nuisance Parameter Is Not Identified Under the Null Hypothesis

This page was built for publication: Are discoveries spurious? Distributions of maximum spurious correlations and their applications