Abstract
An effort has been made to develop calibration estimators of the population mean under two-stage stratified random sampling when auxiliary information is available at primary stage unit level. The properties of the developed estimators are derived in terms of design-based approximate variance and approximate consistent design-based estimator of the variance. Some simulation studies have been conducted to investigate the relative performance of calibration estimators over the usual estimator of the population mean without using auxiliary information in two-stage stratified random sampling. It has been found that the two-step calibration estimator has outperformed than the other calibration estimators and the usual estimator without using auxiliary information.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aditya, K., Sud, U. C., & 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.
Cassel, C. M., Särndal, C. E., & Wretman, J. H. (1976). Some results on generalized difference estimation and generalized regression estimation for finite population. Biometrika, 63, 615–620.
Deville, J. C., & Särndal, C. E. (1992). Calibration estimators in survey sampling. Journal of the American Statistical Association, 87, 376–382.
Estevao, V. M., & Särndal, C. E. (2006). Survey estimates by calibration on complex auxiliary information. International Statistical Review, 74, 127–147.
Horvitz, D. G., & Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47, 663–685.
Kim, J. M., Sunger, E. A., & Heo, T. Y. (2007). Calibration approach estimators in stratified sampling. Statistics and Probability Letters, 77, 99–103.
Mourya, K. K., Sisodia, B. V. S., & Chandra, H. (2016a). Calibration approach for estimating finite population parameter in two-stage sampling. Journal of Statistical Theory and Practice, 10(3), 550–562.
Mourya, K. K., Sisodia, B. V. S., Kumar, S., & Singh, A. (2016b). Calibrated estimators of finite population parameters in equal cluster sampling. International Journal of Agricultural Science, 12, 351–358.
Nidhi, Sisodia, B. V. S., Singh, S., & Singh, S. K. (2016). Calibration approach estimation of mean in stratified sampling and stratified double sampling. Communication in Statistics-Theory and Methods, 46(10), 4932–4942.
Särndal, C. E. (2007). The calibration approach in survey theory and practice. Survey Methodology, 33(2), 99–119.
Särndal, C. E., Swensson, B., & Wretman, J. (2003). Model-assisted survey sampling. New York: Springer.
Singh, S., Horn, S., & Yu, F. (1998). Estimation of variance of the general regression estimators: Higher level calibration approach. Survey methodology, 24(1), 41–50.
Singh, S., Horn, S., Chodhury, S., & Yu, F. (1999). Calibration of the estimators of variance. Australian & New Zealand Journal of Statistics, 41(2), 199–212.
Singh, D., Sisodia, B. V. S., Rai, V. N., & Kumar, S. (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, 71(3), 217–224.
Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S. and Asok, C. (1984). Sampling theory of surveys with applications. Iowa State University Press, Ames, Iowa and Indian Society of Agricultural Statistics, New Delhi.
Tracy, D. S., Singh, S., & Arnab, R. (2003). Note on calibration estimators in stratified and double sampling. Survey Methodology, 29, 99–106.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Sisodia, B.V.S., Singh, D. (2020). Calibration Approach-Based Estimators for Finite Population Mean in Multistage Stratified Random Sampling. In: Chandra, G., Nautiyal, R., Chandra, H. (eds) Statistical Methods and Applications in Forestry and Environmental Sciences. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-1476-0_7
Download citation
DOI: https://doi.org/10.1007/978-981-15-1476-0_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-1475-3
Online ISBN: 978-981-15-1476-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)