Ranked Set Sampling for Small Area Estimation using Auxiliary Data:  Insights from Crop Production Data

Anoop Kumar; Shashi Bhushan; Rohini Pokhrel

doi:10.56093/jisas.v78i03.171413

Authors

Anoop Kumar Central University of Haryana, Mahendergarh
Shashi Bhushan University of Lucknow, Lucknow
Rohini Pokhrel Dr. Shakuntala Misra National Rehabilitation University, Lucknow

https://doi.org/10.56093/jisas.v78i03.171413

Keywords:

Small area estimation; Ranked set sampling; Mean square error; Efficiency.

Abstract

Small area estimation (SAE) is a critical statistical approach used to generate credible estimates for subpopulations or regions with small sample numbers. In agricultural research, reliable crop production estimation at small geographical scales is critical for policy development, resource allocation, and decision-making. Ranked set sampling (RSS), which is recognised for being a cost-effective and accurate data gathering method, is combined with auxiliary data to increase accuracy of the estimates for small regions. This study proposes synthetic ratio type estimators by combining RSS with auxiliary information to improve SAE efficiency and precision, notably in agricultural production estimation. The mean square error (MSE) of the proposed synthetic estimator is obtained to the first order approximation. The approach uses auxiliary information to lower the MSE of the estimators. Comparative investigations with certain well-known adapted SAE estimators reveal that using RSS and auxiliary data considerably improves estimation accuracy for small regions. The theoretical results are supported with a simulation study carried out over an artificially rendered
population. The practical benefits of the suggested estimator are demonstrated by an application to crop production data. The findings indicate that this technique is not only more efficient, but also highly applicable in real-world agricultural surveys, making it a useful tool for improving small area estimates in resource-constrained contexts.

Downloads

Download data is not yet available.

References

Al-Omari, A.I. and Bouza, C. (2015). Ratio estimators of the population mean with missing values using ranked set sampling. Environmetrics, 26(2), 67-76.

Al-Saleh, M.F. and Samawi, H. (2000). On the efficiency of Monte Carlo methods using steady state ranked simulated samples. Communications in Statistics-Simulation and Computation, 29, 941-954.

Ahmed, S., Albalawi, O. and Shabbir, J. (2024). On indirect estimation of small area parameters under ranked set sampling. Alexandria Engineering Journal, 107, 690-697.

Al-Omari, A.I., Jemain, A.A. and Ibrahim, K. (2009). New ratio estimators of the mean using simple random sampling and ranked set sampling methods. Investigacin Operacional, 30(2), 97-108.

Ashutosh, A., Stefan, M., Rai, P.K., Emam, W., Iftikhar, S. and Anas, M.M. (2024). Simulation analysis of non-respondent information in context of small domain. Heliyon, 10(6), e26897.

Bhushan, S. and Kumar, A. (2022a). On the quest of optimal class of estimators using ranked set sampling. Scientia Iranica. doi:10.24200/sci.2022.58063.5547

Bhushan, S. and Kumar, A. (2022b). New efficient logarithmic estimators using multi auxiliary information under ranked set sampling. Concurrency and Computation: Practice and Experience, 34(27), e7337.

Bhushan, S. and Kumar, A. (2023). Imputation of missing data using multi auxiliary information under ranked set sampling. Communications in Statistics-Simulation and Computation, 1-22.

Bhushan, S. and Kumar, A. (2024a). Ranked set sampling imputation methods in presence of correlated measurement errors. Communications in Statistics-Theory and Methods, 1-22.

Bhushan, S. and Kumar, A. (2024b). Novel logarithmic imputation methods under ranked set sampling. Measurement: Interdisciplinary Research and Perspectives, 22(3), 235-257.

Chen, Z., Bai, Z. and Sinha, B. (2004). Ranked set sampling: Theory and Applications. Springer Verlag, New York.

Cochran, W.G. (1977). Sampling techniques. John Wiley & Sons Inc.

Dell, T.R. and Clutter, J.L. (1972). Ranked set sampling theory with order statistics background. Biometrics, 28, 545-555.

Khare, B.B. and Ashutosh (2018). Simulation study of the generalized synthetic estimator for domain mean in the sample survey. International Journal of Tomography & Statistics, 31(3), 87-100.

Kocyigit, E.G. (2023). A novel sub-type mean estimator for ranked set sampling with dual auxiliary variables. Journal of New Theory, 44, 79-86.

Kumar, A., Bhushan, S., Emam, W., Tashkandy, Y. and Khan, M.J.S. (2024a). Novel logarithmic imputation procedures using multi auxiliary information under ranked set sampling. Scientific Reports, 14(1), 18027.

Kumar, A., Bhushan, S., Pokhrel, R. and Emam, W. (2024b). Small area estimation using design based direct and synthetic logarithmic estimators. Ain Shams Engineering Journal, 102836.

Kumar, A., Bhushan, S., Pokhrel, R., Emam, W., Tashkandy, Y. and Khan, M.J.S. (2024c). Enhanced direct and synthetic estimators for domain mean with simulation and applications. Heliyon, 10(14), e33839. https://doi.org/10.1016/j.heliyon.2024.e33839

McIntyre, G.A. (1952). A method of unbiased selective sampling using ranked set. Aust. J. Agr. Res., 3, 385-390.

Mahdizadeh, M. and Zamanzade, E. (2022). Using a rank-based design in estimating prevalence of breast cancer. Soft Computing, 26(7), 3161-3170.

Pandey, K.K. and Tikkiwal, G.C. (2010). Generalized class of synthetic estimators for small area under systematic sampling design. Statistics in Transition- New Series, 11(1), 75-89.

Patil, G.P., Sinha, A.K. and Taillie, C. (1994). Ranked set sampling for multiple characteristics. International Journal of Ecology and Environmental Sciences, 20, 357-373.

Punia, P., Raj, A. and Kumar, P. (2024). An enhanced Beluga Whale optimization algorithm for engineering optimization problems. Journal of Systems Science and Systems Engineering, 1-38.

Rai, P.K. and Pandey, K.K. (2013). Synthetic estimators using auxiliary information in small domains. Statistics in Transition- New Series, 14(1), 31-44.

Raj, A., Punia, P. and Kumar, P. (2024). A novel hybrid pelican-particle swarm optimization algorithm (HPPSO) for global optimization problem. International Journal of System Assurance Engineering and Management, 1-16.

Rao, J.N.K. and Molina, I. (2015). Small area estimation. John Wiley & Sons.

Rehman, S.A. and Shabbir, J. (2022). An efficient class of estimators for finite population mean in the presence of non-response under ranked set sampling (RSS). PLOS ONE, 17(12), e0277232.

Samawi, H.M. and Muttlak, H.A. (1996). Estimation of ratio using ranked set sampling. Biometrical Journal, 38, 753-764.

Searls, D.T. (1964). The utilization of a known coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59(308), 1225-1226.

Stokes, S.L. (1977). Ranked set sampling with concomitant variables. Communications in Statistics-Theory and Methods, A(6), 1207-1211.

Stokes, S.L. and Sager, T.W. (1988). Characterization of a ranked-set sample with application to estimating distribution functions. Journal of the American Statistical Association, 83, 374-381.

Tikkiwal, G.C. and Ghiya, A. (2000). A generalized class of synthetic estimators with application to crop acreage estimation for small domains. Biometrical Journal, 42, 865-876.

Tikkiwal, G.C., Rai, P.K. and Ghiya, A. (2013). On the performance of generalized regression estimator for small domains. Communications in Statistics-Simulation and Computation, 42(4), 891-909.

Zamanzade, E. and Al-Omari, A.I. (2016). New ranked set sampling for estimating the population mean and variance. Hacettepe Journal of Mathematics and Statistics, 45(6), 1891-1905.