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One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…

Statistics Theory · Mathematics 2020-11-24 Morgane Austern , Vasilis Syrgkanis

The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…

Methodology · Statistics 2023-06-21 Henry Lam , Zhenyuan Liu

Bootstrapping is often applied to get confidence limits for semiparametric inference of a target parameter in the presence of nuisance parameters. Bootstrapping with replacement can be computationally expensive and problematic when…

The bootstrap is a popular method of constructing confidence intervals due to its ease of use and broad applicability. Theoretical properties of bootstrap procedures have been established in a variety of settings. However, there is limited…

Statistics Theory · Mathematics 2024-04-19 Zhou Tang , Ted Westling

Consider $M$-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found…

Statistics Theory · Mathematics 2011-02-04 Guang Cheng , Jianhua Z. Huang

The bootstrap is a versatile inference method that has proven powerful in many statistical problems. However, when applied to modern large-scale models, it could face substantial computation demand from repeated data resampling and model…

Methodology · Statistics 2022-02-02 Henry Lam

The bootstrap is a popular and convenient method for quantifying the authority of an empirical ordering of attributes, for example of a ranking of the performance of institutions or of the influence of genes on a response variable. In the…

Statistics Theory · Mathematics 2009-11-20 Peter Hall , Hugh Miller

An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…

Methodology · Statistics 2019-04-10 Thomas Pitschel

Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance…

Applications · Statistics 2012-02-16 Lorna Taylor , Verena M. Trenkel , Vojtech Kupca , Gunnar Stefansson

The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…

Methodology · Statistics 2023-02-16 Yingying Ma , Chenlei Leng , Hansheng Wang

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These…

Statistics Theory · Mathematics 2013-02-19 Joseph P. Romano , Azeem M. Shaikh

A key tool to carry out inference on the unknown copula when modeling a continuous multivariate distribution is a nonparametric estimator known as the empirical copula. One popular way of approximating its sampling distribution consists of…

Statistics Theory · Mathematics 2023-02-01 Ivan Kojadinovic , Kristina Stemikovskaya

The bootstrap, introduced by Efron (1982), has become a very popular method for estimating variances and constructing confidence intervals. A key insight is that one can approximate the properties of estimators by using the empirical…

Methodology · Statistics 2019-01-29 Guido Imbens , Konrad Menzel

Several new methods have been proposed for performing valid inference after model selection. An older method is sampling splitting: use part of the data for model selection and part for inference. In this paper we revisit sample splitting…

Statistics Theory · Mathematics 2018-04-04 Alessandro Rinaldo , Larry Wasserman , Max G'Sell , Jing Lei

Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness…

Econometrics · Economics 2025-10-09 Giuseppe Cavaliere , Iliyan Georgiev

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…

Nuclear Theory · Physics 2019-05-22 A. Pastore

Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…

Methodology · Statistics 2022-08-19 Qian Zhao , Emmanuel J. Candes

Fitting parametric models by optimizing frequency domain objective functions is an attractive approach of parameter estimation in time series analysis. Whittle estimators are a prominent example in this context. Under weak conditions and…

Statistics Theory · Mathematics 2021-07-26 Jens-Peter Kreiss , Efstathios Paparoditis

Constructing tests or confidence regions that control over the error rates in the long-run is probably one of the most important problem in statistics. Yet, the theoretical justification for most methods in statistics is asymptotic. The…

Methodology · Statistics 2019-01-23 Stéphane Guerrier , Mucyo Karemera , Samuel Orso , Maria-Pia Victoria-Feser

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…

Statistics Theory · Mathematics 2019-01-08 Zhonglei Wang , Jae Kwang Kim , Liuhua Peng
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