Resampling methods: Bootstrap background

Since $\widehat{\theta} = \widehat{\theta}(\hat{X})$ is a function of random variables, $\widehat{\theta}$ itself must be a random variable. Thus it has a pdf, call this function $p(\hat{t})$. The aim of the bootstrap is to estimate $p(\hat{t})$ by the relative frequency of $\widehat{\theta}$. You can think of this as using a histogram in the place of $p(\hat{t})$. If the relative frequency closely resembles $p(\vec{t})$, then using numerics, it is straight forward to estimate all the interesting parameters of $p(\hat{t})$ using point estimators.

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