Evaluation of bootstrap methods for coverage estimation and prediction accuracy with small samples

Small sample sizes are common in biomedical research, often making it difficult, or even impossible, to determine the underlying distribution of the data. Traditional frequentist methods typically rely on assumptions of normality, which may not hold in such settings. Bootstrap methods offer a flexible alternative when normality cannot be reasonably assumed, though their use is typically associated with larger sample sizes. This article investigates the performance of four bootstrap methods—nonparametric predictive inference bootstrap (NPI-B), Banks bootstrap (Banks-B), Hutson bootstrap (Hutson-B), and Efron bootstrap (Efron-B)—for estimating population characteristics and making predictive inferences with small sample sizes. A simulation study is conducted using data generated from normal, lognormal, exponential, and mixed-normal distributions. Results indicate that the nonparametric predictive inference bootstrap method performs best for predictive inference with small samples. Additionally, the study highlights promising results for the smooth bootstrap methods, Banks-B and Hutson-B, particularly in the context of estimation.