Related papers: Asymptotics of the Empirical Bootstrap Method Beyo…
Model misspecification is ubiquitous in data analysis because the data-generating process is often complex and mathematically intractable. Therefore, assessing estimation uncertainty and conducting statistical inference under a possibly…
The construction of confidence regions for parameter vectors is a difficult problem in the nonparametric setting, particularly when the sample size is not large. The bootstrap has shown promise in solving this problem, but empirical…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…
This guide aims at providing a general introduction to bootstrap methods. By using simple examples taken from nuclear physics, I discuss how such a method can be used to quantify error bars of an estimator. I also investigate the use of…
Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…
The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends…
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…
Mack's distribution-free chain ladder reserving model belongs to the most popular approaches in non-life insurance mathematics. Proposed to determine the first two moments of the reserve, it does not allow to identify the whole distribution…
Asymptotic uniform confidence bands are constructed for a multivariate nonparametric regression model with heteroscedastic noise, employing histogram estimators under flexible partition conditions. The construction is especially applicable…
The block bootstrap approximates sampling distributions from dependent data by resampling data blocks. A fundamental problem is establishing its consistency for the distribution of a sample mean, as a prototypical statistic. We use a…
This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…
The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics,…
The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to…
There are some papers which describe the use of bootstrap techniques in point process statistics. The aim of the present paper is to show that the form in which bootstrap is used there is dubious. In case of variance estimation of pair…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator of the population mean. For variance estimation,…
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…
Let $\mathbf{X}=(X_1,X_2,X_3)$ be a spherically symmetric random vector of which only $(X_1,X_2)$ can be observed. We focus attention on estimating F, the distribution function of the squared radius $Z:=X_1^2+X_2^2+X_3^2$, from a random…
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…
Income inequality measures are often used as an indication of economic health. How to obtain reliable confidence intervals for these measures based on sampled data has been studied extensively in recent years. To preserve confidentiality,…