Question: Let {Y i } be independent Poisson random variables. Show by the delta method that the estimated asymptotic variance of a i log(Y i )

Let {Y_i} be independent Poisson random variables. Show by the delta method that the estimated asymptotic variance of ∑a_i log(Y_i) is ∑a²_i/y_i. [This formula applies to ML estimators of parameters for the saturated loglinear model, which are contrasts of {log(y_i)}. Formula (14.9) yields the asymptotic covariance structure of such estimators.]

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