On the Asymptotic Relative Efficiencies of Certain Location Parameter Estimates

If, by analogy with means and medians, one computes that value such that the sum of the absolute pth powers of the sample deviations about that point takes on its minimum, one obtains an estimate of the central value of a symmetric distribution. Such estimates, for p ⩽ 1 and under reasonable conditions, are known to be asymptotically normal as the sample size becomes large, and here the asymptotic relative efficiency of any pair is obtained, both for the general case and when the distribution sampled is also supposed unimodal.