Special Issue "Re-sampling Methods for Statistical Inference of the 2020s"

Dear Colleagues,

Re-sampling methods are previous century fellows, with the Bootstrap, no doubt, being the most popular among them, now well into its forties. Following the rocketing evolution of technology, computational power and data sharing, statistical inference as we knew it at the beginning of the twenty-first century, has extraordinary expanded its scope and applications, and the global Covid-19 crisis appears to have even accelerated the process. With this Special Issue I am soliciting contributions, advancements and critical reviews on Bootstrap and re-sampling methods that address the statistical needs of the 2020s and envision future research directions. Manuscripts covering, though not limited to, topics in data science, statistical learning, statistical modelling, epidemiology, observational studies, circular economy, sustainable development and inequalities are particularly welcome.

I look forward to receiving your submissions.

Sincerely,

Prof. Dr. Fulvia Mecatti
Guest Editor

Message from Prof. Bradley Efron:

This is a propitious moment for Stats' special issue on resampling methods. Data sets are bigger than ever, computation is faster and cheaper than ever, and the demand for statistical analysis seems to multiply every year. Computer-intensive statistical methods — the substitution of computational power for routine and tedious paper and pencil calculations — is a growth industry in the current scientific environment, particularly as the complexity of our estimators and tests have outpaced theory.

Resampling plans were the original computer-intensive statistical methodology  (so named in Efron and Diaconis' 1983 Scientific American article.) Their widespread adaptation encouraged other computer-based success stories, Markov Chain Monte Carlo being particularly notable. The term "resampling", in its current sense, seems to have been introduced in the title of my 1982 monograph "The jackknife, the bootstrap, and other resampling plans". Besides the jackknife and the bootstrap, several older resampling methods were discussed there: cross-validation, half-sampling, typical value theory, the infinitesimal jackknife, and balanced repeated replications.

The resampling story of the last forty years has been one of new uses more than new methods. The original, modest, goal of computationally attaching standard errors to statistical estimators was expanded to bootstrap confidence intervals (paralleling an ambitious theoretical development of likelihood based intervals.) Bootstrap smoothing ,aka "bagging" or "bootstrap aggregation", aimed at improving unsmooth estimators such as those obtained from model selection, and became central to Leo Breiman's popular machine learning package "random forests". Massive prediction algorithms, especially "deep learning", required new cross-validation techniques carried out at Herculean scales. As we will see in this volume, applications of resampling have spread to an enormous variety of scientific studies, generating a diversity of specialized techniques as well as an improved theoretical understanding of how the methods perform.

To say that this is a good time for publishing a resampling issue doesn't mean it's easy to do so. I'm grateful to Professor Fulvia Mecatti for conceiving, organizing, and carrying out the task so successfully.

Bradley Efron

Stanford

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Stats is an international peer-reviewed open access quarterly journal published by MDPI.

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• estimation
• big data
• public health
• data integration
• sampling statistics
• statistical assessment
• model selection
• empirical bayes
• population studies

Title: Bayesian bootstrap in multiple frames

Author: Daniela Cocchi, Lorenzo Marchi, Riccardo Ievoli

Abstract: Multiple frames are becoming more and more relevant due to the spread of surveys conducted via registers. Estimators of population quantities at this regard have been proposed in the literature, especially for dual frames, e.g. the multiplicity type estimator. However, variance estimation still remains under debate, especially when frames are more than two. This paper explores the potential of Bayesian bootstrap techniques for computing the variance of this type of estimators in multiple frames. The suitability of the method, which is compared to the existing frequentist bootstrap, is shown through a small-scale simulation study and empirical applications. Despite the lack of closed forms for the variance of estimators in multiple survey, the proposal represents a straightforward solution that, moreover, is not computationally demanding.

Title: Conditional inference in small sample scenarios

Author: Clemens Draxler and Andreas Kurz

Abstract: This paper discusses a non-parametric resampling technique in the context of multidimensional hypothesis testing of assumptions of the Rasch model based on conditional distributions. It is suggested in small sample size scenarios, in which asymptotic theory is not applicable, to approximate the exact sam-pling distribution of various well-known chi square test statistics like Wald, likelihood ratio, score and gradient tests as well as others. A procedure to compute the power function of the tests is also presented. A number of exam-ples of scenarios are discussed in which the power function does not converge to 1 with an increasing deviation from the hypothesis to be tested, i.e. the respective assumption of the model. Finally, an attempt to modify the critical region of the test is made aiming at improving the power.