James-Stein Estimator

Problem

Return the James-Stein shrunken means grand + max(0, 1 - (k-3)*sigma_sq/(n*sum((m-grand)^2)))*(m-grand) for k group means. When k < 3, n <= 0, or all means equal, return the original means unchanged.

Hint

The shrinkage factor is clamped at zero so estimates never overshoot the grand mean.

Test cases

case 1

in: [[12,10,8],10,4,10]

expected: [12,10,8]

case 2

in: [[12,11,9,8],10,4,10]

expected: [11.92,10.96,9.04,8.08]

case 3

in: [[15,10,5],10,1,10]

expected: [15,10,5]

case 4

in: [[20,0,10,10],10,100,1]

expected: [15,5,10,10]

case 5

in: [[20,0,10,10],10,100,0.1]

expected: [10,10,10,10]

Starter codePython

def james_stein(means, grand_mean, sigma_sq, n):
    # Your code here
    pass

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