Canonical Estimation in a Rare-Events Regime
The authors propose a general methodology for performing statistical inference within a 'rare-events regime' that was recently suggested by Wagner, Viswanath and Kulkarni. Their approach allows one to easily establish consistent estimators for a very large class of canonical estimation problems, in a large alphabet setting. These include the problems studied in the original paper, such as entropy and probability estimation, in addition to many other interesting ones. They particularly illustrate this approach by consistently estimating the size of the alphabet and the range of the probabilities.