You have two unbiased estimates e1 and e2 of a quantity, Ask an Expert

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You have two unbiased estimates, e₁ and e₂, of a quantity with variances V₁ and V₂ respectively, and covariance Cov{e1,e₂} = C. Form a new unbiased estimate:

e₃ = a₁e₁+ a₂e₂

Find a₁ and a₂ to minimize the variance of e₃.

1. What is the variance of e₃?

2. Specialize to the case V₁ = V₂ = V and C = cV.

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M9161601

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