The distribution of the sample mean X¯ n from a Cauchy distribution is also Cauchy and jackknifing is not viable. Why? Suppose that the density f(x; θ) has a jump discontinuity at θ (as the population...

The distribution of the sample mean X¯ n from a Cauchy distribution is also Cauchy and jackknifing is not viable. Why?

Suppose that the density f(x; θ) has a jump discontinuity at θ (as the population median). Bootstrapping may not work out in that case, although it can be modified to do so.