In the previous exercise, instead of the Laplace density, consider a logistic density function and conclude on the parallel results on M n and Y n . Consider a distribution F, symmetric about θ and...

In the previous exercise, instead of the Laplace density, consider a logistic density function and conclude on the parallel results on M_n
and Y_n.

Consider a distribution F, symmetric about θ and having a finit support
  where

  Suppose that F has a terminal contact of order m. Defin the kth midrange

 and Theorem 7.7.5 to derive the asymptotic distribution of the normalized form of Mnk . Compute the variance from this asymptotic distribution and denote this by Vm(k), for k > 1. Show that, for m = 1, V1(k) is non-decreasing in k, whereas for m ≥ 2, an opposite inequality may hold.