Related papers: Concentration of the bootstrap empirical process, …
This paper studies posterior concentration behavior of the base probability measure of a Dirichlet measure, given observations associated with the sampled Dirichlet processes, as the number of observations tends to infinity. The base…
Bootstrapping can produce confidence levels for hypotheses about quadratic regression models - such as whether the U-shape is inverted, and the location of optima. The method has several advantages over conventional methods: it provides…
Nonparametric two-sample testing is a classical problem in inferential statistics. While modern two-sample tests, such as the edge count test and its variants, can handle multivariate and non-Euclidean data, contemporary gargantuan datasets…
Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that…
We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…
This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but…
We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…
To use control charts in practice, the in-control state usually has to be estimated. This estimation has a detrimental effect on the performance of control charts, which is often measured for example by the false alarm probability or the…
In a two-stage cluster sampling procedure, $n$ random populations are drawn independently from independent populations and a sub-sample of observations is taken in each of them. The estimator of the general mean of the observed variables is…
We investigate properties of a bootstrap-based methodology for testing hypotheses about equality of certain characteristics of the distributions between different populations in the context of functional data. The suggested testing…
Finkelstein-Schoenfeld, Buyse, Pocock, and other authors have developed generalizations of the Mann-Whitney test that allow for pairwise patient comparisons to include a hierarchy of measurements. Various authors present either asymptotic…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the…
The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer…
We investigate the problem of approximate Bayesian inference for a general class of observation models by means of the expectation propagation (EP) framework for large systems under some statistical assumptions. Our approach tries to…
Concentration of measure has been argued to be the fundamental cause of adversarial vulnerability. Mahloujifar et al. presented an empirical way to measure the concentration of a data distribution using samples, and employed it to find…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
The paper presents a novel approach for unsupervised techniques in the field of clustering. A new method is proposed to enhance existing literature models using the proper Bayesian bootstrap to improve results in terms of robustness and…
Bootstrap is a useful tool for making statistical inference, but it may provide erroneous results under complex survey sampling. Most studies about bootstrap-based inference are developed under simple random sampling and stratified random…
Linear mixed effects are considered excellent predictors of cluster-level parameters in various domains. However, previous work has shown that their performance can be seriously affected by departures from modelling assumptions. Since the…