Question: 35. Let X1, . . . , Xn be a random sample from a pdf that is symmetric about . An estimator for that has

35. Let X1, . . . , Xn be a random sample from a pdf that is symmetric about . An estimator for that has been found to perform well for a variety of underlying distributions is the Hodges–Lehmann estimator. To define it, first compute for each i j and each j 1, 2, . . . , n the pairwise average Xi,j (Xi Xj

)/2. Then the estimator is ˆ the median of the Xi,js. Compute the value of this estimate using the data of Exercise 44 of Chapter 1. [Hint: Construct a square table with the xis listed on the left margin and on top. Then compute averages on and above the diagonal.]

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