Asymptotic Mean Squared Error of Sample Median

Abstract

Asymptotic mean squared error of sample medians, and more generally, sample quantiles, is extremely messy and laborious to calculate, and was previously known up to the second-order. The algebraic chore can now be easily overcome with the help of symbolic languages such as Maple or Mathematica. We obtain the expansion to the third and higher order, and was surprised at some of the implications.