On Combining Ratio and Product Type Estimators For Estimation of Finite Population Mean In Adaptive Cluster Sampling Design
Main Article Content
Abstract
This article introduces a novel class of estimators and several new novel member estimators, combining the ratio and product forms, within the framework of Adaptive Cluster Sampling (ACS) design for estimating finite population mean. Specifically designed for rare or hidden clustered populations, the new novel estimators developed from the proposed class offer enhanced efficiency in estimation. To study the proposed class comprehensively, we derive expressions for the bias and Mean Squared Error (MSE) up to the first order of approximation. Through comprehensive simulation studies, we demonstrate the superior efficiency of the new developed estimators over several existing alternatives considered in this study.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
References
Bahl, S. & Tuteja, R. Ratio and product type exponential estimators. Journal of information and optimization sciences 12, 159–164 (1991). https://doi.org/10.1080/02522667.1991.10699058
Chutiman, N. Adaptive cluster sampling using auxiliary variable. Journal of Mathematics and Statistics 9, 249–255 (2013). http://dx.doi.org/10.3844/jmssp.2013.249.255
Cochran, W. The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. The journal of agricultural science 30, 262–275 (1940). https://doi.org/10.1017/S0021859600048012
Dryver, A. L. & Chao, C.-T. Ratio estimators in adaptive cluster sampling. Environmetrics: The Official Journal of the International Environmetrics Society 18, 607–620 (2007). https://doi.org/10.1002/env.838
Grover, L. K. & Kaur, P. An improved estimator of the finite population mean in simple random sampling. Model Assisted Statistics and Applications 6, 47–55 (2011). http://dx.doi.org/10.3233/MAS-2011-0163
Gupta, S. & Shabbir, J. On improvement in estimating the population mean in simple random sampling. Journal of Applied Statistics 35, 559–566 (2008). https://doi.org/10.1080/02664760701835839
Khoshnevisan, M, Singh, R., Chauhan, P. & Sawan, N. A general family of estimators for estimating population mean using known value of some population parameter (s) (Infinite Study, 2007).
Qureshi, M. N., Kadilar, C., Noor Ul Amin, M. & Hanif, M. Rare and clustered population estimation using the adaptive cluster sampling with some robust measures. Journal of Statistical Computation and Simulation 88, 2761–2774 (2018). https://doi.org/10.1080/00949655.2018.1486842
Singh, H. P. & Solanki, R. S. Improved estimation of finite population variance using auxiliary information. Communications in Statistics-Theory and Methods 42, 2718–2730 (2013). https://doi.org/10.1080/03610926.2011.617485
Singh, H. P., Solanki, R. S. & Singh, A. K. A generalized ratio-cum-product estimator for estimating the finite population mean in survey sampling. Communications in Statistics-Theory and Methods 45, 158–172 (2016). https://doi.org/10.1080/03610926.2013.827719
Thompson, S. K. Adaptive cluster sampling. Journal of the American Statistical Association 85, 1050–1059 (1990). https://doi.org/10.2307/2289601
Thompson, S. K. Sampling (John Wiley & Sons, 2012).
Yadav, S. K., Misra, S., Mishra, S. S. & Chutiman, N. Improved ratio estimators of population mean in adaptive cluster sampling. J. Stat. Appl. Prob. Lett 3, 1–6 (2016). http://dx.doi.org/10.18576/jsapl/030101