Huber Location One Step

Problem

Perform one step of Huber's M-estimator for location: start at the median, compute the scale 1.4826*MAD, form weights that are 1.0 within c*scale and c*scale/abs(deviation) beyond, and return median + sum(w*dev)/sum(w). Return 0.0 for empty data and the median when the scale or total weight is zero.

Hint

This is a single iteratively reweighted least squares update.

Test cases

case 1

in: [[1,2,3,4,5],1.345]

expected: 3

case 2

in: [[1,2,3,10,11],1.345]

expected: 4.223220825333151

case 3

in: [[5,5,5],1.345]

expected: 5

case 4

in: [[],1.345]

expected: 0

case 5

in: [[1,2,3,4,100],1.345]

expected: 3

Starter codePython

def huber_one_step(data, c):
    # Your code here
    pass

5 test cases · run your code against them in the editor