The Hodges–Lehmann location estimator can be defined as the root of the Wilcoxon statistic                    W(µ) = n i=1 sign(Xi − µ)rank(|Xi − µ|). (a) Design an algorithm to compute the estimator...

The Hodges–Lehmann location estimator can be defined as the root of the Wilcoxon statistic

                   W(µ) = n i=1 sign(Xi − µ)rank(|Xi − µ|).

(a) Design an algorithm to compute the estimator that would need to sort only once.

(b) When n modulo 4 is 0 or 3, the estimator is the midpoint of the interval of roots of W. How would you handle that?