Estimating the population median using only a central subset of observations

In estimating the population median, it is common to encounter estimators which are linear combinations of a small number of central observations. Sample medians, sample quasi medians, trimmed means, jackknifed (and delete‐d jackknifed) medians and jackknifed quasi medians are all familiar examples. The objective of this paper is to show that within this class the quasi medians turn out to have the best asymptotic mean squared error.