Bootstrap Inference¶
In this section we document how to use the bootstrap to approximate the distribution of statistics of interest on a given sample.
The main idea of the bootstrap is to combine three steps: Firstly, generate bootstrap samples by drawing from the original data set with replacement. Secondly, calculating the statistic of interest from these resampled data, and finally, using the various estimates to draw inference on the distribution of the true statistic of interest.
Parts of the bootstrap functionality is based on Daniel Saxton’s resample library [Sax18]. It has been adjusted to allow for the additional confidence interval types “bc”, “basic” and “normal”. Moreover, it is faster.
The main bootstrap function takes care of all three steps and returns a table containing means, standard errors and confidence intervals for the estimated parameters.
However, the steps can also be called separately by the user, as described in what follows.
The module implements the first step of drawing B bootstrap samples in two separate ways. The first, and default, method, is to simply draw observations from the original dataset with replacement. The second method is a cluster robust bootstrap, often called pairs cluster bootstrap, that draws clusters, defined by observations with the same value of some specified stratum variable, from the original dataset with replacement. Sample drawing is implemented by drawing seeds. To be as memory-efficient as possible, the actual drawing of data points is by default deferred to the calculation of statistics. However, it is possible to get a list of drawn resampled datasets using
The drawing of samples and calculation of statistics is handled by the following function:
To calculate mean, standard deviation, and a confidence interval of the statistic of interest from the bootstrap outcomes, we can use
The supported types of confidence are explained in more detail here: Bootstrap Confidence Intervals.
- Sax18
Daniel Saxton. Resample: randomization-based inference in python. unpublished, 2018. URL: https://github.com/dsaxton/resample.