Applications of the Fractional-Random-Weight Bootstrap

TL;DR

This paper reviews the fractional-random-weight bootstrap method, demonstrating its advantages over traditional resampling bootstrap, especially in challenging scenarios like censored data, rare events, and near-saturated models, providing a practical alternative for confidence interval estimation.

Contribution

It introduces and demonstrates the fractional-random-weight bootstrap as a robust alternative to resampling bootstrap in difficult data situations.

Findings

Fractional-random-weight bootstrap avoids issues with censored and rare event data.

It provides reliable confidence intervals where resampling bootstrap fails.

The method is easy to implement and advantageous in complex applications.

Abstract

The bootstrap, based on resampling, has, for several decades, been a widely used method for computing confidence intervals for applications where no exact method is available and when sample sizes are not large enough to be able to rely on easy-to-compute large-sample approximate methods, such a Wald (normal-approximation) confidence intervals. Simulation based bootstrap intervals have been proven useful in that their actual coverage probabilities are close to the nominal confidence level in small samples. Small samples analytical approximations such as the Wald method, however, tend to have coverage probabilities that greatly exceed the nominal confidence level. There are, however, many applications where the resampling bootstrap method cannot be used. These include situations where the data are heavily censored, logistic regression when the success response is a rare event or where there is insufficient mixing of successes and failures across the explanatory variable(s), and designed experiments where the number of parameters is close to the number of observations. The thing that these three situations have in common is that there may be a substantial proportion of the resamples where is not possible to estimate all of the parameters in the model. This paper reviews the fractional-random-weight bootstrap method and demonstrates how it can be used to avoid these problems and construct confidence intervals. For the examples, it is seen that the fractional-random-weight bootstrap method is easy to use and has advantages over the resampling method in many challenging applications.