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A prediction approach in adaptive sampling

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Abstract

Adaptive cluster sampling (ACS) due to Thompson (J Am Stat Assoc 85(412):1050–1059, 1990) is a tool to survey rare and hidden elements in a population as an improvement over traditional survey procedures. In ACS, if an observed sampled unit satisfies the given criterion of rarity, its neighboring units are added to the sample and this is continued until one is detected with no rarity. Chaudhuri (Calcutta Stat Assoc Bull 50(3–4):238–253, 2000) extended the above to unequal probability sampling as Adaptive sampling. In practice, often network sizes turn out too big demanding high cost and time. So, Chaudhuri et al. (J Stat Plan Inference 121: 175–189, 2004) gave a subsampling technique to restrict the sample size in Adaptive Sampling. Towards this end, Chaudhuri et al. (J Stat Plan Inference 134: 254–267, 2005) developed a sample size restriction technique. But in Adaptive sampling, capturing neighboring rare units turn out difficult because of various hazards. We propose to try Royall’s (Biometrika 57: 377–389, 1970) prediction approach here to model features of uncaptured network units. We employ Brewer’s (J Am Stat Assoc 74 (368): 911–915, 1979) model-assisted approach to derive a predictor with asymptotic design unbiasedness based on unequal probability samples and examine its efficacy by simulations.

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References

  1. Brewer, K.R.: Ratio estimation an ratio estimation and finite populations: some results deducible from the assumption of an underlying stochastic process. Austral. J. Stat. 5(3), 95–105 (1963)

    Article  MathSciNet  Google Scholar 

  2. Brewer, K.R.: A class of robust sampling designs for large-scale surveys. J. Am. Stat. Assoc. 74, 911–915 (1979)

    Article  MathSciNet  Google Scholar 

  3. Brown, J.A., Manly, B.J.: Restricted adaptive cluster sampling. Environ. Ecol. Stat. 5, 49–63 (1998). https://doi.org/10.1023/A:1009607403647

    Article  Google Scholar 

  4. Cassel, C.M., Sarndal, C.E., Wretman, J.H.: Some results on generalized difference estimation and generalized regression estimation for finite population. Biometrika 63, 615–620 (1976)

    Article  MathSciNet  Google Scholar 

  5. Chaudhuri, A.: Network and adaptive sampling for unequal probabilities. Calcutta Stat. Assoc. Bull. 50, 237–253 (2000)

    Article  MathSciNet  Google Scholar 

  6. Chaudhuri, A., Stenger, H.: Survey Sampling: Theory and Methods, 2nd edn. Chapman and Hall, CRC Press, Taylor & Francis Group, New York (2005)

    Book  Google Scholar 

  7. Chaudhuri, A., Bose, M., Dihidar, K.: Sample size-restrictive adaptive sampling: an application in estimating localized elements. J. Stat. Plan. Inference 134, 254–267 (2005)

    Article  MathSciNet  Google Scholar 

  8. Chaudhuri, A., Bose, M., Ghosh, J.K.: An application of adaptive sampling to estimate highly localized population segments. J. Stat. Plan. Inference 121, 175–189 (2004)

    Article  MathSciNet  Google Scholar 

  9. Chutiman, N., Chiangpradit, M.: Ratio estimator in adaptive cluster sampling without replacement of networks. J. Probab. Stat. 14(2), 1–6 (2014)

    Article  MathSciNet  Google Scholar 

  10. Felix-Medina, M.H., Thompson, S.K.: Adaptive cluster double sampling. Biometrika 91, 877–891 (2004)

    Article  MathSciNet  Google Scholar 

  11. Gattone, S.A., Mohamed, E., Dryver, A.L., Munnich, R.T.: Adaptive cluster sampling for negatively correlated data. Environmetrics 27(2), 103–113 (2016)

    Article  MathSciNet  Google Scholar 

  12. Gattone, S., Mohamed, E., Di, B.T.: Adaptive cluster sampling with clusters selected without replacement and stopping rule. Environ. Ecol. Stat. 23, 453–468 (2016)

    Article  MathSciNet  Google Scholar 

  13. Hansen, M.M., Hurwitz, W.N.: On the theory of sampling from finite populations. Ann. Math. Stat. 14, 333–362 (1943)

    Article  MathSciNet  Google Scholar 

  14. Horvitz, D.G., Thompson, D.J.: An generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc. 47, 663–685 (1952)

    Article  MathSciNet  Google Scholar 

  15. Lahiri, D.B.: A method of sample selection providing unbiased ratio estimates. Bull. Int. Stat. Inst. 3(2), 133–140 (1951)

    MATH  Google Scholar 

  16. Latpate, R.V., Kishirsagar, J.: Negative adaptive cluster sampling. Model Assist. Stat. Appl. 14, 65–81 (2019)

    Google Scholar 

  17. Latpate, R.V., Kshirsagar, J.K.: Negative adaptive cluster double sampling. Stat. Appl. 16, 115–131 (2018)

    Google Scholar 

  18. Lee, K.: Two phase adaptive cluster sampling with unequal probabilities selection. J. Korean Stat. Soc. 27, 265–278 (1998)

    MathSciNet  Google Scholar 

  19. Midzuno, H.: On the sampling system with probability proportional to the sum of the sizes. Ann. Inst. Stat. Math. 3, 99–107 (1952)

    Article  MathSciNet  Google Scholar 

  20. Royall, R.M.: On finite population sampling theory under certain linear regression models. Biometrika 57, 377–389 (1970)

    Article  Google Scholar 

  21. Sarndal, C.E., Swensson, D.E., Wretman, J.H.: Model Assisted Survey Sampling. Springer, New York (1992)

    Book  Google Scholar 

  22. Seber, G.A., Salehi, M.M.: Adaptive sampling designs inference for sparse and clustered populations. Springer (2013). https://doi.org/10.1007/978-3-642-33657-7

    Article  MATH  Google Scholar 

  23. Sen, A.R.: On the estimator of the variance in sampling with varying probabilities. J. Indian Soc. Agric. Stat. 5, 119–127 (1952)

    Google Scholar 

  24. Thompson, S.K.: Adaptive cluster sampling. J. Am. Stat. Assoc. 85, 1050–1059 (1990). https://doi.org/10.1080/01621459.1990.10474975

    Article  MathSciNet  MATH  Google Scholar 

  25. Thompson, S.K.: Adaptive cluster sampling: designs with primary and secondary units. Biometrics 47, 1103–1115 (1991). https://doi.org/10.2307/2532662

    Article  Google Scholar 

  26. Thompson, S.K.: Stratified adapative cluster sampling. Biometrika 78, 389–397 (1991). https://doi.org/10.2307/2337266

    Article  MathSciNet  Google Scholar 

  27. Thompson, S.K.: Sampling. Wiley (1992)

  28. Thompson, S.K., Seber, G.A.: Adaptive Sampling. Wiley, New York (1996)

    MATH  Google Scholar 

  29. Valliant, R., Dorfman, A.H., Royall, R.M.: Finite Population Sampling and Inference: A Prediction Approach. Wiley, New York (2000)

    MATH  Google Scholar 

  30. Yates, F., Grundy, P.: Selection without replacement from within strata with probabilities proportion to size. J. R. Stat. Soc. Ser. B 15, 235–261 (1953)

    MATH  Google Scholar 

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Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Statistics, West Bengal State University, Kolkata, India

    Sanghamitra Pal

  2. West Bengal State University, Kolkata, India

    Dipika Patra

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  1. Sanghamitra Pal
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  2. Dipika Patra
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Correspondence to Sanghamitra Pal.

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Pal, S., Patra, D. A prediction approach in adaptive sampling. METRON 79, 93–108 (2021). https://doi.org/10.1007/s40300-020-00195-1

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