Let X 1 , . . . , X n be a random sample from a pdf that is symmetric about . An

Question

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 HodgesLehmann estimator. To define it, first compute for each i j and each j = 1, 2, . . . , n the pairwise average

Xi,j = (Xi + Xj)/2.

Xi,j's.

Compute the value of this estimate using the data below. [Hint: Construct a square table with the xi's listed on the left margin and on top. Then compute averages on and above the diagonal.]

Please show steps/explain!

28.3 29.5 26.4 30.7 23.6 29.6 28.1 49.4 31.7 34.0

Explanation / Answer

Now we find median of the values in the second column. M=28.7

xi pairwise average Xij 28.3 28.9 29.5 27.95 26.4 28.55 30.7 27.15 23.6 26.6 29.6 28.85 28.1 38.75 49.4 40.55 31.7 32.85 34 17

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