Visualizing the Median as the Minimum-Deviation Location

Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median

Bahadur Representations for the Median Absolute Deviation and Its Modifications

The median absolute deviation about the median (MAD) is an important univariate spread measure having wide appeal due to its highly robust sample version. A powerful tool in treating the asymptotics of a statistic is a linearization, i.e., a Bahadur representation. Here we establish both strong and weak Bahadur representations for the sample MAD. The strong version is the first in the literatur...

The Conditional Location of a Median Path

In this paper, we study the problem of locating a median path of limited length on a tree under the condition that some existing facilities are already located. The existing facilities may be located at any subset of vertices. Upper and lower bounds are proposed for both the discrete and continuous models. In the discrete model, a median path is not allowed to contain partial edges. In the cont...

A Novel Hybrid Modified Binary Particle Swarm Optimization Algorithm for the Uncertain p-Median Location Problem

Here, we investigate the classical p-median location problem on a network in which the vertex weights and the distances between vertices are uncertain. We propose a programming model for the uncertain p-median location problem with tail value at risk objective. Then, we show that it is NP-hard. Therefore, a novel hybrid modified binary particle swarm optimization algorithm is presented to obtai...

Using Local Median as the Location of the Prior Distribution in Iterative Emission Tomography Image Reconstruction

Iterative reconstruction algorithms like MLEM (Maximum Likelihood Expectation Maximization) can be regularized using a weighted roughness penalty term according to certain a priori assumptions of the desired image. In the MRP (Median Root Prior) algorithm the penalty is set according to the deviance of a pixel from the local median. This allows both noise reduction and edge preservation. The pr...