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Sequential Analysis
Design Methods and Applications
Volume 40, 2021 - Issue 2
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Research Article

Minimum risk point estimation of the size of a finite population under mark–recapture strategy

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Pages 243-258 | Received 14 Feb 2020, Accepted 19 Sep 2020, Published online: 12 May 2021

REFERENCES

  • Amstrup, S. C., T. L. McDonald, and B. F. J. Manly. 2010. Handbook of Capture-Recapture Analysis. Princeton, NJ: Princeton University Press.
  • Anscombe, F. J. 1952. “Large-Sample Theory of Sequential Estimation.” Mathematical Proceedings of the Cambridge Philosophical Society 48 (4):600–7. doi:10.1017/S0305004100076386
  • Chow, Y. S., and H. Robbins. 1965. “On the Asymptotic Theory of Fixed Width Sequential Confidence Intervals for the Mean.” The Annals of Mathematical Statistics 36 (2):457–62. doi:10.1214/aoms/1177700156
  • Darling, D. A., and H. Robbins. 1967. “Finding the Size of a Finite Population.” The Annals of Mathematical Statistics 38 (5):1392–938. doi:10.1214/aoms/1177698695
  • Ghosh, M., and N. Mukhopadhyay. 1976. “On Two Fundamental Problems of Sequential Estimation.” Sankhyā, Series B 38:203–18.
  • Ghosh, M., and N. Mukhopadhyay. 1979. “Sequential Point Estimation of the Mean When the Distribution is Unspecified.” Communications in Statistics - Theory and Methods 8 (7):637–52. doi:10.1080/03610927908827789
  • Ghosh, M., and N. Mukhopadhyay. 1981. “Consistency and Asymptotic Efficiency of Two-Stage and Sequential Procedures.” Sankhyā, Series A 43:220–7.
  • Ghosh, M., N. Mukhopadhyay, and P. K. Sen. 1997. Sequential Estimation. New York: Wiley.
  • Goodman, L. A. 1953. “Sequential Sampling Tagging for Population Size Problems.” The Annals of Mathematical Statistics 24 (1):56–69. doi:10.1214/aoms/1177729082
  • Govindarajulu, Z. 2002. “Accelerated Sequential Estimation of the Mean.” American Journal of Mathematical and Management Sciences 22 (1-2):99–113. doi:10.1080/01966324.2002.10737578
  • Hall, P. 1983. “Sequential Estimation Saving Sampling Operations.” Journal of the Royal Statistical Society: Series B (Methodological) 45 (2):219–23. doi:10.1111/j.2517-6161.1983.tb01243.x
  • Jolly, G. M. 1965. “Explicit Estimates from Capture-Recapture Data with Both Death and IMMIGRATION-STOCHASTIC MODEL.” Biometrika 52:225–47. doi:10.2307/2333826
  • King, R., and S. P. Brooks. 2008. “On the Bayesian Estimation of a Closed Population Size in the Presence of Heterogeneity and Model Uncertainty.” Biometrics 64 (3):816–24. doi:10.1111/j.1541-0420.2007.00938.x
  • Lebreton, J. D., K. P. Burnham, J. Clobert, and D. R. Anderson. 1992. “Modeling Survival and Testing Biological Hypotheses Using Marked Animals: A Unified Approach with Case Studies.” Ecological Monographs 62 (1):67–118. doi:10.2307/2937171
  • Mukhopadhyay, N. 1996. “An Alternative Formulation of Accelerated Sequential Procedures with Applications to Parametric and Nonparametric Estimation.” Sequential Analysis 15 (4):253–69. doi:10.1080/07474949608836363
  • Mukhopadhyay, N., and D. Bhattacharjee. 2018. “Sequentially Estimating the Required Optimal Observed Number of Tagged Items with Bounded Risk in the Recapture Phase under Inverse Binomial Sampling.” Sequential Analysis 37 (3):412–29. doi:10.1080/07474946.2018.1548851
  • Mukhopadhyay, N., and B. M. de Silva. 2009. Sequential Methods and Their Applications. Boca Raton, FL: CRC.
  • Mukhopadhyay, N., and T. K. S. Solanky. 1991. “Second Order Properties of Accelerated Stopping Times with Applications in Sequential Estimation.” Sequential Analysis 10 (1-2):99–123. doi:10.1080/07474949108836228
  • Peterson, C. G. J. 1896. “The Yearly Immigration of Young Plaice into the Limfjord from the German Sea.” Report of Danish Biological Station 6:1–48.
  • Robbins, H. 1959. “Sequential Estimation of the Mean of a Normal Population.” In Probability and Statistics, H. Cramér Volume, U. Grenander, 235–45. Uppsala, Sweden: Almquist and Wiksell.
  • Scheaffer, R. L., W. Mendenhall, III, R. L. Ott, and K. G. Gerow. 2012. Elementary Survey Sampling, 7th ed. Boston, MA: Brooks/Cole.
  • Schnabel, Z. E. 1938. “The Estimation of the Total Fish Population of a Lake.” The American Mathematical Monthly 45 (6):348–52. doi:10.1080/00029890.1938.11990818
  • Seber, G. A. F. 1965. “A Note on the MULTIPLE-RECAPTURE CENSUS.” Biometrika 52:249–59. doi:10.2307/2333827
  • Silva, I. R., D. Bhattacharjee, and N. Mukhopadhyay. 2020. Numerical versus Asymptotic Sequential Interval Estimation of Population Sizes, submitted.
  • Wiener, N. 1939. “The Ergodic Theorem.” Duke Mathematical Journal 5 (1):1–18. doi:10.1215/S0012-7094-39-00501-6
  • Wilson, B., P. S. Hammond, and P. M. Thompson. 1999. “Estimating Size and Assessing Trends in a Coastal Bottlenose Dolphin Population.” Ecological Applications 9 (1):288–300. doi:10.1890/1051-0761(1999)009[0288:ESAATI2.0.CO;2]
  • Woodroofe, M. 1982. Nonlinear Renewal Theory in Sequential Analysis, CBMS 39. Philadelphia, PA: SIAM.
  • Zacks, S. 2009. Stage-Wise Adaptive Designs. New York: Wiley.

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