Consider the model i = , i = 1,..., n, for independent Poisson observations. For = y, show that the model-based asymptotic variance

Consider the model µ_i = β, i = 1,..., n, for independent Poisson observations. For β̂ = y̅, show that the model-based asymptotic variance estimate is y̅/n, whereas the robust estimate of the asymptotic variance is ∑_i (y_i – y̅)²/n². Which would you expect to be better (a) if the Poisson model holds, and (b) if there is severe overdispersion?