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.