## Summary

Statistical inference to evaluate the uncertainty/variability of estimations is usually challenging in classical statistics. But this is not true when resampling methods are used, data-oriented methods to make valid inference, perfectly suited for data scientists.

The bootstrap is a general tool to estimate the variance of an estimator. The estimation of the variance of a very complex statistic is as easy as estimating the variance of a simple estimator such as the arithmetic mean.

We saw that another popular resampling method – the jackknife – is by far not as trustable as the bootstrap, especially for non-smooth estimators. However, the jackknife is a useful tool to estimate the variance of the bootstrap variance estimate, for example.

Cross validation is very similar to the jackknife, but its aim is different. With cross validation, models can be compared and the prediction error is in the foreground.

Especially the bootstrap is now - in the next chapter - applied to practical more...