ESTIMATING VARIANCE IN THE PRESENCE OF NONRESPONSE UNDER UNEQUAL PROBABILITY SAMPLING WITHOUT REPLACEMENT
Keywords:
Probability proportional to size sampling, first and second order inclusion probability, sampling fraction, reverse frameworkAbstract
In this paper we propose 2 estimators for estimating a population total under unequal probability sampling without replacement, a linear and a ratio estimator. We show in theory that the linear estimator is an unbiased estimator and the latter is an asymptotically unbiased estimator. We propose a general form of the variance, and also an estimator of the variance in this paper considered under the reverse framework and only when the sampling fraction is negligible. We can show in theory that the variance estimators of the proposed estimators are asymptotically unbiased. A simulation study has been conducted to ascertain the performance of the proposed estimators.
References
Berger, Y.G. ( 2005) . Variance estimation with Chao's sampling scheme. J. Stat. Plan. Infer., 127:253-277.
Bethlehem, J.G. (1988) . Reduction of nonresponse bias through regression estimation. J. Off. Stat. , 3:251- 260.
Deville, J. C. and Särndal, C. E. ( 1995) . Variance estimation for the regression imputed Horvitz- Thompson estimator. J. Off. Stat., 4:381-394.
Fay, R.E. (1991). A design-based perspective on missing data variance. Proceedings of the 1991 US Bureau of the Census Annual Research Conference; March 17-20, 1991; Arlington, VA, USA, p. 447-450.
Hájek, J. (1981). Sampling in Finite Population. Marcel Dekker, New York, NY, USA, 264p.
Horvitz, D.F. and Thompson, D.J. (1952). A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc., 260:663-685.
Kajal, D. (2014) . Estimating population mean with missing data in unequal probability sampling. Statistics in Transition, 3:369-388.
Lawson, N. (2017). Variance estimation in the presence of nonresponse under probability proportional to size sampling. Proceedings of 6th Annual International Conference on Computational Mathematics, Computational Geometry & Statistics; March 6-7, 2017; Singapore; p. 116:119.
Lawson, N. and Ponkaew, C. (2019) . New generalized regression estimator in the presence of nonresponse under unequal probability sampling. Comm. Stat. A-Theor., 48(10):2,483-2,498,
Midzuno, H. (1952). On sampling system with probability proportional to sum of sizes. Ann. I. Stat. Math. , 3:99-107.
Särndal, C.E. (1992).Method for estimating the precision of survey estimates when imputation has been used. Surv. Methodol., 2:241-252.
Särndal, C.E. and Lundström, S. (2005) . Estimation in Surveys with Nonresponse. John Wiley & Sons, Chichester, UK, 194p.
Shao, J. and Steel, P. ( 1999) . Variance estimation for survey data with composite imputation and nonnegligible sampling fractions. J. Am. Stat. Assoc., 94:54-265.
Thompson, K. J. , Yung, W. , and Haziza, D. (2010) . The effect of nonresponse adjustments on variance estimation. Surv. Methodol., 36:35-43.
Tillé, Y. and Matei, A. (2009). The package “sampling”. R contributed package. Retrieved from https://cran. r-project.org/web/packages/sampling/sampling.pdf.
