Asymptotic normality of a nonparametric estimator of sample coverage

Annals of Statistics

Volumn 37, Issue 5 A, 2009, Pages 2582-2595

  Zhang, Cun Hui ^a   Zhang, Zhiyi ^b  

^a RUTGERS UNIVERSITY   (United States)

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

Author keywords

Asymptotic normality; Sample coverage; Turing's formula

Indexed keywords

EID: 69049092745     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS658     Document Type: Article

References (20)

1. Chao, A. (1981). On estimating the probability of discovering a new species. Ann. Statist. 9 1339-1342. MR0630117
2. Chao, A. (1984). Nonparametric estimation of the number of the classes in a population. Scand. J. Statist. 11 265-270. MR0793175
3. Chao, A. and Lee, S. (1992). Estimating the number of classes via sample covergae. J. Amer. Statist. Assoc. 87 210-217. MR1158639
4. Efron, B. and Thisted, R. (1976). Estimating the number of unseen species: How many words did Shakespeare know? Biometrika 63 435-447.
5. Esty, W. W. (1982). Confidence intervals for the coverage of low coverage samples. Ann. Statist. 10 190-196. MR0642730
6. Esty, W. W. (1983). A normal limit law for a nonparametric estimator of the coverage of a random sample. Ann. Statist. 11 905-912. MR0707940
7. Esty, W. W. (1985). Estimation of the number of classes in a population and the coverage of a sample. Math. Sci. 10 41-50. MR0801156
8. Esty, W. W. (1986a). The size of a coinage. Numismatic Chronicle 146 185-215. MR0925622
9. Esty, W. W. (1986b). The efficiency of Good's nonparametric coverage estimator. Ann. Statist. 14 1257-1260. MR0856822
10. Good, I. J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika 40 237-264. MR0061330
11. Good, I.J. and Toulmin, G.H. (1956). The number of new species, and the increase in population coverage, when a sample is increased. Biometrika 43 45-63. MR0077039
12. Harris, B. (1959). Determining bounds on integrals with applications to cataloging problems. Ann. Math. Statist. 30 521-548. MR0102876
13. Harris, B. (1968). Statistical inference in the classical occupancy problem, unbiased estimation of the number of classes. J. Amer. Statist. Assoc. 63 837-847. MR0231480
14. Holst, L. (1981). Some assymptotic results for incomplete multinomial or Poisson samples. Scand. J. Statist. 8 243-246. MR0642805
15. Mao, C.X. and Lindsay, B. G. (2002). A Poisson model for the coverage problem with a genomic application. Biometrika 89 669-681. MR1929171
16. Quackenbush, J., Cho, J., Lee, D., Liang, F., Holt, I., Karamycheva, S., Parvizi, B., Pertea, G., Sultana, R. and White, J. (2001). The TIGR gene indices: Analysis of gene transcript sequences in highly sampled eukaryotic species. Nucleic Acids Res. 29 159-164.
17. Robbins, H. E. (1968). Estimating the total probability of the unobserved outcomes of an experiment. Ann. Statist. 39 256-257. MR0221695
18. Starr, N. (1979). Linear estimation of probability of discovering a new species. Ann. Statist. 7 644-652. MR0527498
19. Thisted, R. and Efron, B. (1987). Did Shakespeare write a newly-discovered poem? Biometrika 74 445-455. MR0909350
20. Zhang, C.-H. (2005). Estimation of sums of random variables: Examples and information bounds. Ann. Statist. 33 2022-2041. MR2211078