# Bootstrap resampling

## Bootstrap Resampling

Bootstrap resampling is a statistical technique to measure the error in a given statistic that has been computed from a sample population. It is a simple yet powerful methord that relies heavily on computational power. The basic premise is that instead of using a theoretical or mathematical model for the parent distribution from which our observed samples were drawn from, we can use the distribution of the observed samples as an approximation for the parent distribution.

### The Algorithm

Let’s say we observe ${\displaystyle N}$ data samples, denoted as ${\displaystyle {\vec {x}}=(x_{1},x_{2},x_{3},...,x_{N})}$, and we want to compute a statistic ${\displaystyle {\hat {\theta }}=s({\vec {x}})}$. This statistic ${\displaystyle s}$ could be the mean or median of our samples, but could also be something much more complex. In measuring ${\displaystyle {\hat {\theta }}}$ from our data, we want to know how close our estimator is to the true value, denoted by ${\displaystyle \theta _{\mathrm {true} }}$.