ML Anthology

Asymptotic Properties of Turing's Formula in Relative Error

Michael Grabchak, Zhiyi Zhang
MLJ 2017 pp. 1771-1785
doi:10.1007/S10994-016-5620-6 /mlj/2017/grabchak2017mlj-asymptotic/

Abstract

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 $\alpha \in (0,1]$ α ∈ ( 0 , 1 ] .

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Text

Grabchak and Zhang. "Asymptotic Properties of Turing's Formula in Relative Error." Machine Learning, 2017. doi:10.1007/S10994-016-5620-6

Markdown

[Grabchak and Zhang. "Asymptotic Properties of Turing's Formula in Relative Error." Machine Learning, 2017.](https://mlanthology.org/mlj/2017/grabchak2017mlj-asymptotic/) doi:10.1007/S10994-016-5620-6

BibTeX

@article{grabchak2017mlj-asymptotic,
  title     = {{Asymptotic Properties of Turing's Formula in Relative Error}},
  author    = {Grabchak, Michael and Zhang, Zhiyi},
  journal   = {Machine Learning},
  year      = {2017},
  pages     = {1771-1785},
  doi       = {10.1007/S10994-016-5620-6},
  volume    = {106},
  url       = {https://mlanthology.org/mlj/2017/grabchak2017mlj-asymptotic/}
}