In this exercise we will further explore the ARE of the median to the mean, ARE(Mn, ).
(a) Verify the three AREs given in Example 10.2.4.
(b) Show that ARE(Mn, ) is unaffected by scale changes. That is, it doesn't matter whether the underlying pdf is f(x) or (1/σ)f(x/σ).
(c) Calculate ARE(Mn, ) when the underlying distribution is Student's t with v degrees of freedom, for v = 3, 5, 10, 25, 50, ˆž. What can you conclude about the ARE and the tails of the distribution?
(d) Calculate ARE(Mn, ) when the underlying pdf is the Tukey model

Calculate the ARE for a range of δ and σ. What can you conclude about the relative performance of the mean and the median?

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