resamplingia

Resamplingia is a conceptual framework in probability and statistics that studies resampling methods and their theoretical properties, with emphasis on robustness of inference under varied data-generating processes. It investigates operations such as bootstrap, permutation tests, cross-validation, and their generalizations, focusing on estimator behavior under resampling.

Origin and scope: It emerged from mid-20th century growth of resampling techniques and has since expanded to cover sampling distributions, bias correction, and simulation-based inference. In practice, it is discussed in model assessment, uncertainty quantification, and nonparametric approaches.

Core ideas include invariance under sampling, coverage accuracy, sample-size effects, dependence structures, and the role of weighting. Resamplingia distinguishes between sampling with and without replacement, and includes weighted and block resampling for dependent data.

Methods and applications: The framework encompasses bootstrap variants, permutation tests, cross-validation, bagging, and jackknife-like schemes. It is used to estimate confidence intervals, p-values, performance metrics, and to stress-test estimators in small samples or irregular conditions.

Critiques and status: As a theoretical construct, resamplingia emphasizes the conditions under which resampling yields reliable inference, noting biases in small samples or with strong dependence or heavy tails. It remains an active area of statistical theory and data-science research.