High-dimensional Bernstein-von Mises theorem for the Diaconis-Ylvisaker prior

DOI10.1016/j.jmva.2023.105279MaRDI QIDQ6189155

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Publication date: 12 January 2024

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

total variation asymptotic normality exponential family density estimation concentration inequality Bernstein-von Mises multinomial-Dirichlet Diaconis-Ylvisaker prior

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Multivariate analysis (62Hxx)

Cites Work

Nonparametric Bernstein-von Mises theorems in Gaussian white noise
The semiparametric Bernstein-von Mises theorem
On the Bernstein-von Mises phenomenon for nonparametric Bayes procedures
Bernstein-von Mises theorems for Gaussian regression with increasing number of regressors
A semiparametric Bernstein-von Mises theorem for Gaussian process priors
An analysis of Bayesian inference for nonparametric regression
Bernstein-von Mises theorem for linear functionals of the density
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
Optimal filtering of square-integrable signals in Gaussian noise
Conjugate priors for exponential families
Asymptotic normality of posterior distributions in high-dimensional linear models
On the Bernstein-von Mises theorem with infinite-dimensional parameters
Asymptotics in statistics. Some basic concepts.
Asymptotic normality of posterior distributions for exponential families when the number of parameters tends to infinity.
Optimal Gaussian approximations to the posterior for log-linear models with Diaconis-Ylvisaker priors
Convergence rates of posterior distributions.
Probability inequalities for likelihood ratios and convergence rates of sieve MLEs
A Bernstein-von Mises theorem for discrete probability distributions
Reference priors for exponential families with increasing dimension
On the Bernstein-von Mises phenomenon in the Gaussian white noise model
Statistical guarantees for Bayesian uncertainty quantification in nonlinear inverse problems with Gaussian process priors
Asymptotic Normality of Semiparametric and Nonparametric Posterior Distributions
Asymptotic Statistics
Mathematical Foundations of Infinite-Dimensional Statistical Models

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