How to Polish off Median Polish

Abstract

Tukey's median polish is an algorithm for smoothing data in two-way tables. Each iteration lowers the $L_1 $ norm of the residual. For commensurable data the algorithm converges in a finite number of steps. It does not, in general, converge to the least $L_1 $ norm residual. We provide an algorithm that converges in a finite number of steps for any real data and gives the least $L_1 $ residual.