Performance of a Predictive Ratio Estimator in Two-Stage Sampling with Auxiliary Inforation
DOI:
https://doi.org/10.33003/fjs-2026-1022-6096Keywords:
Predictive Ratio Estimator, Two-Stage Sampling, Double Sampling, Auxiliary Information, Relative EfficiencyAbstract
This study examines the relative performance of a predictive ratio estimator against the conventional ratio estimator within a two-stage sampling design incorporating double sampling for the auxiliary variable. Fertilizer application quantity was used as the auxiliary characteristic, with crop yield as the study variable. Estimator performance was assessed through the mean squared error (MSE), standard error (SE), coefficient of variation (CV), and relative efficiency (RE). The predictive ratio estimator had a lower MSE of 0.1542, a SE of 0.3927 and a CV of 2.065% against the MSE of 0.1560, a SE of 0.3927 and a CV of 2.092% for the classical ratio estimator. The predictive ratio estimator also yielded a slightly higher relative efficiency of 101.17% compared with classical ratio estimator 100%. This efficiency gain is attributable to the estimator's capacity to exploit the strong auxiliary–study variable correlation captured in the first-phase sample. The study recommends the adoption of predictive ratio estimators in two-stage agricultural surveys with reliable auxiliary data.
References
Al-Omari, A. I. (2012). Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling. Statistics & Probability Letters, 82(11), 1883–1890. https://doi.org/10.1016/j.spl.2012.07.001
Arbia, G., Solano-Hermosilla, G., Micale, F., Nardelli, V., & Genovese, G. (2020). Post-sampling crowdsourced data to allow reliable statistical inference: The case of food price indices in Nigeria. International Journal of Geo-Information, 8(11), 498–505. https://doi.org/10.1038/s41597-023-02211-1
Cochran, W. G. (1977). Sampling techniques (3rd ed.). John Wiley and Sons.
Hidiroglou, M. A., & Särndal, C. E. (1998). Use of auxiliary information for two-phase sampling. Survey Methodology, 24(1), 11–20. statcan.gc.ca
Khan, S., Farooq, M., Ahmed, S., SidAhmed, M. M., Idriss, M. E., Hussain, E. M. M., & Albadwi, F. I. A. (2025). On use of predictive technique for estimation of population mean using auxiliary information: Application on real data sets. European Journal of Pure and Applied Mathematics, 18(2), 6019–6035. https://doi.org/10.29020/nybg.ejpam.v18i2.6019
Kumar, M., & Saini, R. (2020). Exponential estimators for finite population mean using auxiliary attributes under predictive approach. Revista Investigación Operacional, 41(3), 413–420.
Lohr, S. L. (2021). Sampling: Design and analysis (3rd ed.). Chapman and Hall/CRC.
Michael, C. U., & Mbanefo, S. M. (2022). Two-stage cluster sampling with unequal probability sampling in the first stage and ranked set sampling in the second stage. Statistics in Transition New Series, 23(3), 199–214. https://doi.org/10.2478/stattrans-2022-0038
Ozturk, O. (2019). Two-stage cluster samples with ranked set sampling designs. Annals of the Institute of Statistical Mathematics, 71, 63–91. https://doi.org/10.1007/s10463-017-0623-z
Panda, K. B. (2015). An efficient predictive approach to estimation in two-phase sampling. IOSR Journal of Mathematics, 11(3), 78–81.
Saini, M. A. (2013). A class of predictive estimators in two-stage sampling when auxiliary character is estimated at SSU level. International Journal of Pure and Applied Mathematics, 85(2), 285–295. https://doi.org/10.12732/ijpam.v85i2.8
Särndal, C. E., Swensson, B., & Wretman, J. (1992). Model assisted survey sampling. Springer.
Swain, A. K. P. C., Mishra, S. S., and Pradhan, B. K. (2013). On some predictive ratio type estimators in two stage sampling. Journal of Statistical Theory and Applications, 12(1), 83–91. https://doi.org/10.2991/jsta.2013.12.1.7
Yadav, S.K., Mishra, S.S., Kumar, S., Kumar, R., (2018). New Efficient Predictive Estimator of Population Mean using Median of study variable, Jnanabha, 48 (1), 17-25.
Yadav, S. K., & Mishra, P. (2015). Upgraded ratio-cum-product type predictive estimators to estimate the population mean. Statistika: Statistics and Economy Journal, 95(1), 76–85. csu.gov.cz.
Yadav, S. K., Shabbir, J., Pandey, S. K., & Gupta, S. (2018). Predictive estimation of finite population mean using coefficient
of kurtosis and median of an auxiliary variable under simple random sampling scheme. International Journal of Mathematical Archive, 9(5), 137–144.
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Copyright (c) 2026 George Orkuma Akanyi, Jonathan Atsua Ikughur, Tersoo Uba
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