Control Variate Adjusted Estimate

Problem

A control variate estimator is mean(f) - c * (mean(h) - mu_h), where mu_h is the known expectation of the control. For the optimal coefficient c = Cov(f, h) / Var(h), the covariance is Cov(f, h) / Var(h).

Given samples of f, samples of h, the known mean of h, and the coefficient c (default 1.0), return the adjusted estimate.

Hint

Subtract the scaled discrepancy between the sample and known control means.

Test cases

case 1

in: [[1,2,3],[0.5,1,1.5],1]

expected: 2

case 2

in: [[2,4],[1,3],3,0.5]

expected: 3.5

case 3

in: [[0,0],[5,5],5]

expected: 0

Starter codePython

def control_variate_adjusted_estimate(f_samples, h_samples, h_mean, c=1.0):
    # Your code here
    pass

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