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ˆ β = (X T X)1 X T y Var ˆ β = σ 2 (X T X)1 Let ˜ β = 7, a kvector of 7 Var ˜ β = 0, but E ˜ β 6 = β in general The GM Thm says that for any fixed w, Var w T ˆ β 6 Var w T ˜ β where ˜ β is any linear unbiased estimator for β w T Var ˜ β w > w T Var ˆ β w w T You have done everything absolutely correctly, but was not able to find a sum You got n n/2 n/4 , which is equal to n * (1 1/2 1/4 ) You got a sum of geometric series, which is equal to 2Therefore your sum is 2nSo the complexity is O(n) PS this is not called telescoping Telescoping in math is when the subsequent terms cancel each otherSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more



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