Control Variate Variance Reduction

Problem

With the optimal control-variate coefficient, the variance of an estimator is reduced by a factor of 1 - correlation^2 relative to the crude estimator. Return that factor, or 0.0 when the correlation is outside [-1, 1].

Hint

The residual variance after the best linear control is the fraction 1 - rho^2.

Test cases

case 1

in: [0.5]

expected: 0.75

case 2

in: [0.9]

expected: 0.18999999999999995

case 3

in: [0]

expected: 1

case 4

in: [-0.8]

expected: 0.3599999999999999

case 5

in: [1.2]

expected: 0

Starter codePython

def control_variate_variance_reduction(correlation):
    # Your code here
    pass

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