Notes on Use of the Composite Estimator: an Improvement of the Ratio Estimator

Kung-Jong Lui

doi:10.2478/jos-2020-0007

Abstract

This article discusses use of the composite estimator with the optimal weight to reduce the variance (or the mean-squared-error, MSE) of the ratio estimator. To study the practical usefulness of the proposed composite estimator, a Monte Carlo simulation is performed comparing the bias and MSE of composite estimators (with estimated optimal weight and with known optimal weight) with those of the simple expansion and the ratio estimators. Two examples, one regarding the estimation of dead fir trees via an aerial photo and the other regarding the estimation of the average sugarcane acres per county, are included to illustrate the use of the composite estimator developed here.

References

Casella, G. and R.L. Berger. 1990. Statistical Inference. Belmont, CA: Duxbury.
Search in Google Scholar Back to article
Cochran, W.G. 1977. Sampling Techniques (3rd ed.). New York: Wiley.
Search in Google Scholar Back to article
Fleiss, J.L., B. Levin, and M.C. Paik. 2003. Statistical Methods for Rates and Proportions (3rd ed.). New York: Wiley. DOI: https://doi.org/10.1002/0471445428.10.1002/0471445428
Search in Google Scholar Back to article
Govindarajulu, Z. 1999. Elements of Sampling Theory and Methods. Upper Saddle River, NJ: Prentice Hall.
Search in Google Scholar Back to article
Lee, S.E., P.R. Lee, and K-II. Shin. 2016. “A Composite Estimator for Stratified Two-Stage Cluster Sampling.” Communications for Statistical Applications and Methods 23: 47–55. DOI: https://doi.org/10.5351/CSAM.2016.23.1.047.10.5351/CSAM.2016.23.1.047
Search in Google Scholar Back to article
Lui, K.-J. and W.G. Cumberland. 1991. “A Model-Based Approach: Composite Estimators for Small Area Estimation.” Journal of Official Statistics 7: 69–76.
Search in Google Scholar Back to article
Lui, K.-J. 2004. Statistical Estimation of Epidemiological Risk. New York: Wiley. DOI: https://doi.org/10.1002/0470094087.10.1002/0470094087
Search in Google Scholar Back to article
Pascual, J.N. 1961. “Unbiased Ratio Estimators in Stratified Sampling.” Journal of American Statistical Association 56: 70–87. DOI: https://doi.org/10.2307/2282332.10.2307/2282332
Search in Google Scholar Back to article
Royall, R.M. 1970. “On Finite Population Sampling Theory under Certain Linear Regression Models.” Biometrika 57: 377–387. DOI: https://doi.org/10.1093/biomet/57.2.377.10.1093/biomet/57.2.377
Search in Google Scholar Back to article
Sahoo, L.N. 1987. “On a Class of Almost Unbiased Estimators for Population Ratio.” Statistics 18: 119–121. DOI: https://doi.org/10.1080/02331888708801998.10.1080/02331888708801998
Search in Google Scholar Back to article
SAS Institute Inc. 2009. SAS/STAT 9.2 User’s Guide (2nd ed.). Cary, NC: SAS Institute.
Search in Google Scholar Back to article
Schaible, W.L. 1978. “Choosing Weight for Composite Estimators for Small Area Statistics.” In Proceedings of the Section on Survey Research Methods, 741–746. Washington: American Statistical Association.
Search in Google Scholar Back to article
Schaible, W.L. 1979. “A Composite Estimator for Small Area Statistics.” In Proceedings of the Section on Social Statistics, 1017–1021. Washington: American Statistical Association
Search in Google Scholar Back to article
Scheaffer, R.L., W. Mendenhall III, R.L. Ott, and K.G. Gerow. 2012. Elementary Survey Sampling (7th ed.). Boston, MA: Brooks/Cole.
Search in Google Scholar Back to article
Sukhatme, P.V., B.V. Sukhatme, S. Sukhatme, and C. Asok. 1984. Sampling Theory of Surveys Applications (3rd ed.). Ames, Iowa: Iowa State University Press.
Search in Google Scholar Back to article
Thompson, S.K. 2012. Sampling (3rd ed.). New York: Wiley. DOI: https://doi.org/10.1002/9781118162934.10.1002/9781118162934
Search in Google Scholar Back to article

Notes on Use of the Composite Estimator: an Improvement of the Ratio Estimator

Abstract

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