A new non-parametric resampling method based on representative points

As a resampling method, the bootstrap method is a powerful statistical tool that allows for estimating the distribution of a statistic (like the mean, variance, median, etc.) by resampling from the empirical distribution. This method consistently gains significant attention from the statistical community and is particularly useful when the underlying distribution of the data is unknown or when the sample size is too small for the assumptions of traditional parametric methods. In this article, we propose a novel non-parametric resampling method based on representative points (RPs). This resampling method is derived through the techniques of kernel smoothing and draws inspiration from the representative points. Theoretical analysis demonstrates that the convergence of the resampling distribution constructed by the representative points can be guaranteed in the cases of the sample mean and sample variance under the Kolmogorov metric and Mallows-Wasserstein metric. To evaluate the efficiency of the novel method, a comprehensive Monte Carlo numerical study is conducted to compare this method with common non-parametric and parametric bootstrap methods. Simulation results show that it generally improves the performance of non-parametric bootstrap methods in terms of the coverage rate of confidence intervals. Meanwhile, it is competitive in comparison with parametric bootstrap methods, especially for small sample sizes. Two real datasets are analyzed to further illustrate the implementation of the proposed method.