Assessing the multivariate normal approximation of the maximum likelihood estimator from high-dimensional, heterogeneous data

DOI10.1214/18-EJS1492zbMath1406.62019arXiv1510.03679WikidataQ128846502 ScholiaQ128846502MaRDI QIDQ1627568

Andreas Anastasiou

Publication date: 30 November 2018

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

Full work available at URL: https://arxiv.org/abs/1510.03679

zbMATH Keywords

Stein's methodmultivariate normal approximationmulti-parameter maximum likelihood estimation

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (10)

INTEGRATION BY PARTS: AN INTRODUCTION ⋮ TWO-LOOP VACUUM DIAGRAMS IN BACKGROUND FIELD AND THE HEISENBERG–EULER EFFECTIVE ACTION ⋮ Multivariate normal approximation of the maximum likelihood estimator via the delta method ⋮ FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS ⋮ Bounds for the asymptotic distribution of the likelihood ratio ⋮ Bounds in \(L^1\) Wasserstein distance on the normal approximation of general M-estimators ⋮ Fixed point characterizations of continuous univariate probability distributions and their applications ⋮ Wasserstein distance error bounds for the multivariate normal approximation of the maximum likelihood estimator ⋮ SECTOR DECOMPOSITION ⋮ Estimation of smooth functionals in high-dimensional models: bootstrap chains and Gaussian approximation

Uses Software

• gRc

Cites Work

• Optimal-order bounds on the rate of convergence to normality in the multivariate delta method
• Bounds for the normal approximation of the maximum likelihood estimator
• Optimal-order uniform and nonuniform bounds on the rate of convergence to normality for maximum likelihood estimators
• Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
• Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models
• On the existence and uniqueness of the maximum likelihood estimate of a vector-valued parameter in fixed-size samples
• Extremal families and systems of sufficient statistics
• Bounds for the normal approximation of the maximum likelihood estimator from \(m\)-dependent random variables
• Bounds for the asymptotic normality of the maximum likelihood estimator using the Delta method
• Statistical Methods in Markov Chains
• Bayesian precision and covariance matrix estimation for graphical Gaussian models with edge and vertex symmetries
• Asymptotic Properties of Maximum Likelihood Estimators for the Independent Not Identically Distributed Case
• Consistency and Asymptotic Normality of MLE's for Exponential Models
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