Minimax risk for missing mass estimation

The problem of estimating the missing mass or total probability of unseen elements in a sequence of n random samples is considered under the squared error loss function. The worst-case risk of the popular Good-Turing estimator is shown to be between 0.6080/n and 0.6179/n. The minimax risk is shown to be lower bounded by 0.25/n. This appears to be the first such published result on minimax risk for estimation of missing mass, which has several practical and theoretical applications.