An RP-based Resampling Method for the Logistic Distribution and Its Application - Shi, Cuiran; Liang, Xindan; Liang, Jiajuan (International Journal of Statistics in Medical Research, 2025)
This paper proposes a representative point-based bootstrap (RP-bootstrap) to improve confidence interval estimation for the logistic distribution. The method replaces the traditional empirical distribution with a smoothed approximation constructed from statistically optimal representative points (RPs), leading to a more stable resampling distribution. We integrate the RP-bootstrap with the bootstrap-t, percentile, and BCa methods to construct intervals for the location and scale parameters. Its performance is compared to the classical nonparametric bootstrap via comprehensive Monte Carlo simulations and two real-data applications. The results show that the RP-bootstrap delivers noticeable improved finite-sample performance, particularly for small samples where standard bootstrapping often under-covers. It achieves recognizably higher coverage probabilities while maintaining shorter or comparable expected interval lengths. These improvements are strongest for the bootstrap-t interval and are consistent for both parameters, though more marked for the location. In conclusion, the RP-bootstrap is a computationally efficient and reliable alternative for logistic inference, offering enhanced accuracy, especially in small-sample scenarios. Purpose: Construction of confidence intervals under small sample size is frequently encountered in statistical inference, such as estimating some treatment effect in medical research with limited number of patients. Traditional nonparametric bootstrap methods often suffer from undercoverage in such settings. To address this limitation, we propose the RP-bootstrap—a resampling procedure that draws samples from an approximated distribution formed by representative points (RPs) of the logistic distribution. Methods: The RP-bootstrap is developed for constructing confidence intervals for the mean and variance of the logistic distribution. The algorithm generates weighted samples from the estimated RPs. The RP-bootstrap method is applied to construction of different types of confidence intervals (CIs) like the bootstrap-t, percentile, and BCa CIs. Its performance and comparison with the traditional nonparametric bootstrap are evaluated through Monte Carlo simulation and real-data application. Results: Based on the Monte Carlo study under a set of small sample sizes, the RP-bootstrap achieves noticeable higher empirical coverage probability and competitive or shorter expected interval lengths compared with the nonparametric bootstrap. The improvements are much noticeable for small sample sizes like n<30 and for the bootstrap-t confidence intervals, where the nonparametric bootstrap frequently shows undercoverage of the true population parameter. Contribution: This study demonstrates that representative points provide a stable and efficient alternative to resampling methods from logistic models. The RP-bootstrap offers a practical method for reliable small-sample inference and yields confidence intervals with improved accuracy and reduced variability relative to the traditional nonparametric bootstrap method.