Asymptotic properties of Turing’s formula in relative error

摘要

Turing’s formula allows one to estimate the total probability associated with letters from an alphabet, which are not observed in a random sample. In this paper we give conditions for the consistency and asymptotic normality of the relative error of Turing’s formula of any order. We then show that these conditions always hold when the distribution is regularly varying with index \(\alpha \in (0,1]\).