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 a 2 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 ...

The Delta Method is a way to approximate the distribution of a function of a random var ...

Let {Y i } be independent Poisson random variables. Show by the delta method that the estimated

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) 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.]