The Smoothed Bootstrap Fine-Tuning

The bootstrap method is a well-known method to gather a full probability distribution from the dataset of a small sample. The simple bootstrap i.e. resampling from the raw dataset often leads to a significant irregularities in a shape of resulting empirical distribution due to the discontinuity of a support. The remedy for these irregularities is the smoothed bootstrap: a small random shift of source points before each resampling. This shift is controlled by specifically selected distributions. The key issue is such parameter settings of these distributions to achieve the desired characteristics of the empirical distribution. This paper describes an example of this procedure.