Evaluating the Role of Bootstrapping Methods in Estimating Sampling Distributions for Small Data Samples

Posted: Jun 09, 2007

• James Young
• Zoey Baker
• Olivia Walker

Abstract

The challenge of statistical inference from small data samples represents a fundamental problem across numerous scientific disciplines, particularly in emerging fields where data collection is expensive, time-consuming, or ethically constrained. Traditional statistical methods relying on asymptotic theory often prove inadequate when sample sizes fall below conventional thresholds, leading to biased estimates and unreliable inference. Bootstrapping, introduced by Efron in 1979, has revolutionized statistical practice by providing a computationally intensive approach to estimate sampling distributions without stringent distributional assumptions. However, the performance of bootstrap methods in small-sample contexts remains poorly understood, with conflicting evidence in the literature regarding their reliability and optimal implementation. This research addresses a critical gap in statistical methodology by systematically evaluating various bootstrapping approaches specifically designed for small data samples. We define small samples as those with n 30, a range where conventional statistical methods often break down and where bootstrap methods face unique challenges including limited representativeness of the underlying population and increased sensitivity to outliers. The novelty of our approach lies in developing a hybrid framework that integrates parametric, nonparametric, and Bayesian resampling techniques, creating a more robust methodology for small-sample inference. Our primary research questions investigate whether bootstrapping methods can provide reliable estimates of sampling distributions for small samples, which variations perform best under different distributional scenarios, and how the performance varies across different parameters of interest. We challenge the conventional dichotomous classification of bootstrap methods and propose a continuum-based approach that adapts to sample characteristics. Through extensive simulation studies, we provide empirical evidence regarding the conditions under which bootstrap methods succeed or fail in small-sample contexts, offering practical guidance for researchers across disciplines.