The asymptotic distribution of the MLE in high-dimensional logistic models: arbitrary covariance

DOI10.3150/21-BEJ1401MaRDI QIDQ2137045

Emmanuel J. Candès, Qian Zhao, Pragya Sur

Publication date: 16 May 2022

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.09351

zbMATH Keywords

maximum likelihood estimationlogistic regressionhigh-dimensional inferenceGaussian covariates

Mathematics Subject Classification ID

Linear inference, regression (62Jxx) Parametric inference (62Fxx) Multivariate analysis (62Hxx)

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Uses Software

• GitHub
• glmhd

Cites Work

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• On asymptotically optimal confidence regions and tests for high-dimensional models
• High dimensional robust M-estimation: asymptotic variance via approximate message passing
• Statistics for high-dimensional data. Methods, theory and applications.
• On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators
• Fluctuations of eigenvalues and second order Poincaré inequalities
• Asymptotic behavior of M-estimators of p regression parameters when \(p^ 2/n\) is large. I. Consistency
• Asymptotic behavior of M estimators of p regression parameters when \(p^ 2/n\) is large. II: Normal approximation
• Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity
• On parameters of increasing dimensions
• The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression
• Bounds for the asymptotic distribution of the likelihood ratio
• The likelihood ratio test in high-dimensional logistic regression is asymptotically a rescaled Chi-square
• Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
• On robust regression with high-dimensional predictors
• Asymptotic Statistics
• High-Dimensional Statistics
• Precise Error Analysis of Regularized <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math> </inline-formula>-Estimators in High Dimensions
• Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models
• De-Biased Sparse PCA: Inference for Eigenstructure of Large Covariance Matrices
• Semisupervised Inference for Explained Variance in High Dimensional Linear Regression and its Applications
• MEAN FIELD ASYMPTOTICS IN HIGH-DIMENSIONAL STATISTICS: FROM EXACT RESULTS TO EFFICIENT ALGORITHMS
• State evolution for general approximate message passing algorithms, with applications to spatial coupling
• A modern maximum-likelihood theory for high-dimensional logistic regression
• Optimal errors and phase transitions in high-dimensional generalized linear models
• The LASSO Risk for Gaussian Matrices
• Algorithmic Learning Theory
• Gene hunting with hidden Markov model knockoffs
• Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models
• The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses