Let X1 Xn be a random sample from a pdf that is symmetri

Let X₁, . . . , X_n 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

X_i,j = (X_i + X_j)/2.

X_i,j\'s.

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

Please show steps/explain!

Solution

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