Best linear blend of two estimates

Two independent unbiased estimators of the same quantity have variances σ12=1\sigma_1^2 = 1 and σ22=3\sigma_2^2 = 3. What weight ww on the first estimator (and 1w1-w on the second) minimizes the variance of the blend? (to 2 decimals)

Show hints (2)+
  1. Set the derivative of the blended variance to zero.
  2. Weight each estimator proportionally to 1/variance.

Answer

Reveal answer →

0.75

Want the full step-by-step worked solution? It's part of Premium — along with a worked solution for every question in the bank.

Asked at: Jane Street, Two Sigma

Related questions