The Need for Diagnostic Assessment of Bootstrap Predictive Models

Abstract

The bootstrap is, at heart, a way to obtain an approximate sampling distribution for a statistic (and hence, if required, produce a confidence interval). Where that statistic is a suitable estimator for a population parameter of interest, the bootstrap enables inferences about that parameter. In the case of simple situations the bootstrap is very simple in form, but more complex situations can be dealt with. The bootstrap can be modified in order to produce a predictive distribution (and hence, if required, prediction intervals). It is predictive distributions that are generally of prime interest to insurers (because they pay the outcome of the process, not its mean). The bootstrap has become quite popular in reserving in recent years, but it's necessary to use the bootstrap with caution. The bootstrap does not require the user to assume a distribution for the data. Instead, sampling distributions are obtained by resampling the data. However, the bootstrap certainly does not avoid the need for assumptions, nor for checking those assumptions. The bootstrap is far from a cure-all. It suffers from essentially the same problems as finding predictive distributions and sampling distributions of statistics by any other means. These problems are exacerbated by the time-series nature of the forecasting problem - because reserving requires prediction into never-before-observed calendar periods, model inadequacy in the calendar year direction becomes a critical problem. In particular, the most popular actuarial techniques - those most often used with the bootstrap - don't have any parameters in that direction, and are frequently mis-specified with respect to the behaviour against calendar time. Further, commonly used versions of the bootstrap can be sensitive to overparameterization - and this is a common problem with standard techniques. In this paper, we describe these common problems in using the bootstrap and how to spot them.