a) Use the delta method to derive the asymptotic variance expression below Avar(bar()_MLE) = 1/nv_1 [ (_2
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Question:
a) Use the delta method to derive the asymptotic variance expression below
Avar(bar(μ)_MLE) = 1/nv_1 [ (μ_2 (V_2)^2)/ 4c^4 + (μ_3 V_2)/ c^2 + μ_4 - (μ_2)^2 ]
b) Using the definition F^-(1) (t) = inf{ y: F(y) >= t} Serfling gives the result that F(y) >= t if and only if y >= F^-(1) (t) for any distribution function. Use that result to prove: for any distribution function F , the distribution function of F^-(1) (U), where U is a uniform(0,1) random variable, is F(y). That is, show that P(F^-(1) (U) =< y) for all y.
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