Abstract
A general ratio estimator of a population total is proposed as an approximation to the estimator introduced by Srivastava (1985,Bull. Internat. Statist. Inst.,51(10.3), 1–16). This estimator incorporates additional information gathered during the survey in a new way. Statistical properties of the general ratio estimator are given and its relationship to the estimator proposed by Srivastava is explored. A special kind of general ratio estimator is suggested and it turns out to be very efficient in a simulation study when compared to several other commonly used estimators.
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References
Brewer, K. R. W. and Hanif, M. (1983). Sampling with unequal probabilities,Lecture Notes in Statistics,15, Springer, New York.
Hájek, J. (1981).Sampling from a Finite Population, Marcel Dekker, New York.
Ouyang, Z. (1989). Investigation on some estimators and strategies in sampling, proposed by Srivastava, Ph.D. Thesis, Colorado State University, Fort Collins.
Ouyang, Z. and Schreuder, H. T. (1992). Srivastava estimation in forestry,Forest Science (submitted).
Ouyang, Z., Schreuder, H. T. and Li, J. (1991a). Regression estimation under sampling with one unit per stratum,Comm. Statist. Theory Methods,20, 2431–2449.
Ouyang, Z., Schreuder, H. T., Max, T. and Williams, M. (1991b). Poisson-Poisson and binomial-Poisson sampling in forestry,Survey Methodology (submitted).
Raj, D. (1972).Sampling Theory, McGraw-Hill, New York.
Rao, J. N. K. (1979). On deriving mean square errors and their non-negative unbiased estimators in finite population sampling,J. Indian Statist. Assoc.,17, 125–136.
Särndal, C. E. (1980). On π-inverse weighting versus best linear unbiased weighting in probability sampling,Biometrika,67, 639–650.
Schreuder, H. T., Li, H. G. and Hazard, J. W. (1987). PPS and random sampling estimation using some regression and ratio estimators for underlying linear and curvilinear models,Forest Science,33, 997–1009.
Serfling, R. J. (1980).Approximation Theorems of Mathematical Statistics, Wiley, New York.
Srivastava, J. N. (1985). On a general theory of sampling, using experiment design. Concepts I: Estimation,Bull. Internat. Statist. Inst.,51(10.3), 1–16.
Srivastava, J. N. and Ouyang, Z. (1992). Studies on the general estimator in sampling, based on sample weight function,J. Statist. Plann. Inference,31, 177–196.
Sukhatme, P. V., Sukhatme, B. V., Sukhatme, S. and Asok, C. (1984).Sampling Theory of Survey with Application, Iowa State University Press, Ames.
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The work of this author was supported by AFOSR grant #830080.
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Ouyang, Z., Srivastava, J.N. & Schreuder, H.T. A general ratio estimator and its application in model based inference. Ann Inst Stat Math 45, 113–127 (1993). https://doi.org/10.1007/BF00773672
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DOI: https://doi.org/10.1007/BF00773672