A sufficient normality condition for Turing's formula

Journal of Nonparametric Statistics

Volumn 20, Issue 5, 2008, Pages 431-446

  Zhang, Zhiyi ^a   Huang, Hongwei ^a  

^a UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

Asymptotic normality; Turing's formula

Indexed keywords

EID: 47549085934     PISSN: 10485252     EISSN: 10290311     Source Type: Journal    
DOI: 10.1080/10485250802172126     Document Type: Article

References (20)

1. B. Efron and R. Thisted, Estimating the number of unseen species: how many words did Shakespeare know?, Biometrika 63 (1976), pp. 435-447.
2. R. Thisted and B. Efron, Did Shakespeare write a newly-discovered poem?, Biometrika 74 (1987), pp. 445-455.
3. I.J. Good and G.H. Toulmin, The number of new species, and the increase in population coverage, when a sample is increased, Biometrika 43 (1956), pp. 45-63.
4. A. Chao, On estimating the probability of discovering a new species, Ann. Stat. 9 (1981), pp. 1339-1342.
5. C.X. Mao and B.G. Lindsay, A Poisson model for the coverage problem with a genomic application, Biometrika 89 (2002), pp. 669-681.
6. C.-H. Zhang, Estimation of sums of random variables: examples and information bounds, Ann. Stat. 33 (2005), pp. 2022-2041.
7. I.J. Good, The population frequencies of species and the estimation of population parameters, Biometrika 40 (1953), pp. 237-264.
8. B. Harris, Determining bounds on integrals with applications to cataloging problems, Ann. Math. Stat. 30 (1959), pp. 521-548.
9. _, Statistical inference in the classical occupancy problem unbiased estimation of number of classes, J. Am. Stat. Assoc. 63 (1968), pp. 837-847.
10. H.E. Robbins, Estimating the total probability of the unobserved outcomes of an experiment, Ann. Math. Stat. 39 (1968), pp. 256-257.
11. N. Starr, Linear estimation of probability of discovering a new species, Ann. Stat. 7 (1979), pp. 644-652.
12. L. Holst, Some assymptotic results for incomplete multinomial or Poisson samples, Scand. J. Stat. 8 (1981), pp. 243-246.
13. A. Chao, Nonparametric estimation of the number of the classes in a population, Scand. J. Stat. 11 (1984), pp. 265-270.
14. W.W. Esty, Confidence intervals for the coverage of low coverage samples, Ann. Stat. 10 (1982), pp. 190-196.
15. _, A normal limit law for a nonparametric estimator of the coverage of a random sample,Ann. Stat. 11 (1983), pp. 905-912.
16. _, Estimation of the number of classes in a population and the coverage of a sample, Math. Sci. 10 (1985), pp. 41-50.
17. _, The size of a coinage, Numis. Chron. 146 (1986a), pp. 185-215.
18. _, The efficiency of Good's nonparametric coverage estimator, Ann. Stat. 14 (1986b), pp. 1257-1260.
19. A.Chao andS.Lee,Estimating the number of classes via sample covergae,J.Am. Stat.Assoc.87(1992),pp. 210-217.
20. M.S. Bartlett, The characteristic function of a conditional statistic, J. Lond. Math. Soc. 13 (1938), pp. 62-67.