Stein's method compares probability distributions through the study of a class of linear
operators called Stein operators. While mainly studied in probability and used to underpin …

Supplement to “Bootstrapping and sample splitting for high-dimensional, assumption-lean
inference”. This supplement provides additional material, including numerical examples …

Abstract Uniform and nonuniform Berry–Esseen (BE) bounds of optimal orders on the rate of
convergence to normality in the delta method for vector statistics are obtained. The results …

It is well known that, under general regularity conditions, the distribution of the maximum
likelihood estimator (MLE) is asymptotically normal. Very recently, bounds of the optimal …

We use the delta method and Stein's method to derive, under regularity conditions, explicit
upper bounds for the distributional distance between the distribution of the maximum …

We give an asymptotic development of the maximum likelihood estimator (MLE), or any
other estimator defined implicitly, in a way which involves the limiting behavior of the score …

We obtain explicit p-Wasserstein distance error bounds between the distribution of the multi-
parameter MLE and the multivariate normal distribution. Our general bounds are given for …

The asymptotic normality of the maximum likelihood estimator (MLE) under regularity
conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds …

Checking how well a fitted model explains the data is one of the most fundamental parts of a
Bayesian data analysis. However, existing model checking methods suffer from trade-offs …

We obtain bounds to quantify the distributional approximation in the delta method for vector
statistics (the sample mean of $ n $ independent random vectors) for normal and non …