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Variance decomposition in two-stage plot sampling: theoretical and empirical results

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Abstract

The statistical properties of two-stage plot sampling estimators of abundance are considered. In the first stage, some spatial units are selected over the whole study area according to a suitable sampling design, while in the second stage, the selected units are surveyed with floating plot sampling to estimate the abundance within. Some insights into the accuracy of the resulting estimators are obtained by splitting the sample variance into the first and second-stage components, while performance is empirically checked by means of a simulation study. Simulation results show that, in most situations, a relevant amount of the overall variance is due to the second stage sampling.

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References

  • Berger, Y. G. (1998)Rate of convergence to normal distribution for the Horvitz-Thompson estimator. Journal of Statistical Planning and Inference, 74, 149-68.

    Google Scholar 

  • Brewer, K. R. W. and Hanif, M. (1983)Sampling with Unequal Probabilities, Springer-Verlag, Berlin.

    Google Scholar 

  • Caughley, G. (1977)Sampling in aerial survey. Journal of Wildlife Management, 41, 605-15.

    Google Scholar 

  • Chaudhuri, A. and Vos, J. W. E. (1988)Unified Theory and Strategies of Survey Sampling, Amsterdam, North-Holland.

    Google Scholar 

  • Cochran, W. G. (1977)Sampling Techniques, Wiley, New York.

    Google Scholar 

  • De Vries, P. G. (1986)Sampling Theory for Forest Inventory, Springer-Verlag, Berlin.

    Google Scholar 

  • Fattorini, L. and Pisani, C. (2001)Two-stage estimators of animal abundance using sample area surveys, Working Paper n. 27, Dipartimento di Metodi Quantitativi, Universita`di Siena.

  • Hedayat, A. S. and Shina, B. K. (1991)Design and Inference in Finite Population Sampling, Wiley, New York.

    Google Scholar 

  • Jensen, A. L. (1996)Subsampling with line transects for estimation of animal abundance. Environmetrics, 7, 283-9.

    Google Scholar 

  • Lahiri, D. B. (1951)A method of sample selection providing unbiased ratio estimates. Bulletin of the International Statistical Institute, 33, 133-40.

    Google Scholar 

  • Midzuno, H. (1952)On the sampling system with probability proportional to sum of sizes. Annals of the Institute of Statistical Mathematics, 3, 99-107.

    Google Scholar 

  • Pisani, C. (2002)The estimation of biological population size at large scale by incomplete area surveys and replicated counts. Environmetrics, 13, 155-66.

    Google Scholar 

  • Sampford, M. R. (1967)On sampling without replacement with unequal probabilities of selections. Biometrika, 54, 499-513.

    Google Scholar 

  • Schreuder, H. T., Gregoire, T. G., and Wood, G. B. (1993)Sampling Methods for Multire-sources Forest Inventory, Wiley, New York.

    Google Scholar 

  • Scott, A. and Wu, C. (1981)On the asymptotic distribution of ratio and regression estimators. Journal of the American Statistical Association, 76, 98-102.

    Google Scholar 

  • Skalski, J. R. (1994)Estimating wildlife population based on incomplete area surveys. Wildlife Society Bulletin, 22, 192-203.

    Google Scholar 

  • Sutherland, W. J. (1996)The twenty commonest censusing sins, in Ecological Census Techniques, a Handbook, Sutherland W. J. (ed), Cambridge University Press, Cambridge. pp. 317-8.

    Google Scholar 

  • Thompson, S. K. and Seber, G. A. F. (1994)Detectability in conventional and adaptive sampling. Biometrics, 50, 712-24.

    Google Scholar 

Download references

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Fattorini, L., Pisani, C. Variance decomposition in two-stage plot sampling: theoretical and empirical results. Environmental and Ecological Statistics 11, 385–396 (2004). https://doi.org/10.1007/s10651-004-4185-x

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