To give an example where the empirical bootstrap fails, consider the following situation. Suppose our dataset x 1 , x 2 ,...,xn is a realization of a random sample X 1 , X 2 ,...,Xn from a U(0, θ)...

To give an example where the empirical bootstrap fails, consider the following situation. Suppose our dataset x₁, x₂,...,xn is a realization of a random sample X₁, X₂,...,Xn from a U(0, θ) distribution. Consider the normalized sample statistic

strap random sample from the empirical distribution function of our dataset, and let M∗ n be the corresponding bootstrap maximum. We are going to compare the distribution functions of Tn and its bootstrap counterpart