Double Calibration Approach Based Estimator for Population Mean in Two-Stage Stratified Random Sampling When Auxiliary Information Is Available At Element Level

Dhirendra Singh¹ , B.V.S. Sisodia²

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.6 , pp.196-207, Dec-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.196207

Online published on Dec 31, 2018

Copyright © Dhirendra Singh, B.V.S. Sisodia . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Singh et al. (2017) have developed calibration estimators of population mean in two-stage stratified random sampling by calibrating integrated sampling design weight when the auxiliary information is available at element (second stage unit) level for the entire population. Obviously, if the auxiliary information is available at the element level for entire population, then population mean/total of the auxiliary variable is also known. In the present paper, double (two-steps) calibration estimators of the population mean have been developed by calibrating integrated sampling design weight at first step and calibrating stratum weight at the second step using known population total/mean of the auxiliary variable. A limited simulation study with real data has been conducted to examine the relative performance of the calibration estimators over the usual estimator of the population mean without using auxiliary information in two-stage stratified random sampling. It has been found from the results of simulation study that double (two-steps) calibration estimator has brought considerable improvement in the precision of the estimate of population mean.

Key-Words / Index Term :
Calibration Estimator, Auxiliary Information, Two-Stage Sampling, Stratified Random Sampling.

References :
[1]. Aditya, Kaustav., Sud, U.C., and Chandra, H. (2016). Calibration based regression type estimator of the population total under two-stage sampling design. Journal of the Indian Society of Agricultural Statistics, 70 (1), 19-24.
[2]. Deville, J.C. and Särndal, C.E. (1992). Calibration estimators in survey sampling. Journal of the American Statistical Association, 87, 376–382.
[3]. Estevao, V.M. and Särndal, C.E. (2009). A new face on two-phase sampling with calibration estimators. Survey Methodology, 35(1), 3-4.
[4]. Horvitz, D.G. and Thompson, D.J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47, 663-685.
[5]. Kim, J.M., Sunger, E.A. and Heo, T.Y. (2007). Calibration approach estimators in stratified sampling. Statistics and Probability Letters, 77, 99-103.
[6]. Kim, J.K. and Park, M. (2010). Calibration estimation in survey sampling. International Statistical Review, 78, 21-39.
[7]. Mourya, K.K., Sisodia, B.V.S. and Chandra, H. (2016). Calibration approach for estimating finite population parameter in two-stage sampling, Journal of Statistical Theory and Practice, (Online, 19 May 2016).
[8]. Mourya, K.K., Sisodia, B.V.S., Singh, Amar and Rai, V.N. (2016). Calibration estimators in cluster sampling when cluster are of unequal size. Int. J. Agricult. and Statistical Sci., 12(2), 351-358.
[9]. Särndal, C.E., Swensson, B. and Wretman, J. (1992). Model-assisted Survey Sampling. New York: Springer-Verlag.
[10]. Särndal, C.E. (2007). The calibration approach in survey theory and practice. Survey Methodology, 33(2), 99-119.
[11]. Singh, Dhirendra., Sisodia, B.V.S., Kumar, Sunil., and Kumar, Sandeep. (2017). Some calibration estimators for finite population mean in two-stage stratified random sampling. Communication in Statistics- Theory and Methods, (submitted).
[12]. Singh, Dhirendra., Sisodia, B.V.S., Rai, V.N., and Kumar, Sandeep. (2017). A calibration approach based regression and ratio type estimators of finite population mean in two-stage stratified random sampling. Journal of the Indian Society of Agricultural Statistics, (submitted).
[13]. Singh, S., Horn, S. and Yu, F. (1998). Estimation of variance of the general regression estimators: Higher level calibration approach. Survey methodology, 24(1), 41-50.
[14]. Sinha, N., Sisodia, B.V.S., Singh, S. and K. Singh, Sanjay. (2016). Calibration approach estimation of mean in stratified sampling and stratified double sampling. Communication in Statistics- Theory and Methods, (Online, 27 May, 2016).
[15]. Singh, S. and Arnab, R. (2011). On calibration of design weights. Metron, 69(2), 185-205.
[16]. Tracy, D.S., Singh, S. and Arnab, R. (2003). Note on calibration estimators in stratified and double sampling. Survey Methodology, 29, 99-106.