A sufficient normality condition for Turing's formula

Zhiyi Zhang and Hongwei Huang

Journal of Nonparametric Statistics, 2008, vol. 20, issue 5, 431-446

Abstract: This paper establishes a previously unknown sufficient condition for the asymptotic normality of the non-parametric sample coverage estimate based on Good under a fixed underlying probability distribution {pk; k=1, …} where all pk>0. The sufficient condition of this paper supports a non-empty class of distributions and excludes the condition of Esty as a marginal case in which it is shown that the √n-normalised sample coverage estimate proposed by Esty necessarily degenerates under a fixed {pk}. The convergent statistic in the newly established normality law and the resulting relevant confidence intervals are all of new forms, and specifically are different from those suggested by Esty.

Date: 2008
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DOI: 10.1080/10485250802172126

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