New Generalized Regression Estimators Using a Ratio Method and Its Variance Estimation for Unequal Probability Sampling without Replacement in the Presence of Nonresponse
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Abstract
One of the most important problems for planning in economics is that reliable data can be difficult to obtain either because it has not been recorded or because of nonresponse in surveys. This paper is aimed at proposing new generalized regression estimators using the ratio method of estimation for estimating population mean and population total and also variance estimators of the proposed generalized regression estimators in the presence of uniform nonresponse of a study variable. We show in theory that the proposed estimators are almost unbiased under unequal probability sampling without replacement when nonresponse occurs in the study. In the simulation studies, the performances of the proposed estimators were better when compared to the existing ones in terms of minimum relative bias and relative root mean square error. In an application to Thai maize in Thailand with 2019 data, we can see that the proposed estimators gave smaller variance estimates when compared to the existing estimators.
Keywords: ratio estimator; generalized regression estimator; automated linearization approach; response probabilities; nonresponse
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References
Hansen, M.H. and Hurwitz, W.N., 1946. The problem of nonresponse in sample surveys. Journal of the American Statistical Association, 41, 517-529.
Särndal, C.E. and Lundström, S., 2005. Estimation in Surveys with Nonresponse. New York: John Wiley.
Horvitz, D.F. and Thompson, D.J., 1952. A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47(260), 663-685.
Estevao, V.M. and Särndal, C.E., 2006. Survey estimates by calibration on complex auxiliary information. International Statistical Review, 72(2), 127-147.
Chauvet, G., 2016. Variance estimation for the 2006 French housing survey. Mathematical Population Studies, 23(3), 147-163.
Lawson, N. and Ponkaew, C., 2019. New generalized regression estimator in the presence of nonresponse under unequal probability sampling. Communications in Statistics -Theory and Methods, 48(10), 2483-2498.
Lawson, N., 2017. Variance estimation in the presence of nonresponse under probability proportional to size sampling. Proceedings of the 6th Annual International Conference on Computational Mathematics, Computational Geometry and Statistics (CMCGS 2017), Singapore, March 6-7, 2017, pp. 50-54.
Fay, R.E., 1991. Design-based perspective on missing data variance. Proceedings of the 1991 Annual Research Conference: Bureau of the Census, Virginia, USA, March 17-20, 1991, pp. 17-20.
Lawson, N. and Siripanich, P., 2022. A new generalized regression estimator and variance estimation for unequal probability sampling without replacement for missing data. Communications in Statistics -Theory and Methods, 51(18), 6296-6318.
Cochran, W.G., 1977. Sampling Techniques. 3rd ed. New York: John Wiley.
Bacanli, S. and Kadilar, C., 2008. Ratio estimators with unequal probability designs. Pakistan Journal of Statistics, 24(3), 167-172.
Ponkaew, C. and Lawson, N., 2018. A new ratio estimator for population total in the presence of nonresponse under unequal probability sampling without replacement. Thai Journal of Mathematics; Special Issue (2018): Asian Conference on Fixed Point Theory and Optimization 2018, 417-429.
Midzuno, H., 1952. On the sampling system with probability proportional to sum of sizes. Annals of the Institute of Statistical Mathematics, 4(3), 99-107.
R Core Team, 2021. R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing.