Multivariate ratio exponential estimators of the population mean under stratified double sampling. (English) Zbl 1514.62021
Summary: To estimate the population mean when sampling a heterogeneous population and in the absence of a priori information on auxiliary variables, exponential-ratio multivariate estimators are associated under double stratified sampling with two auxiliary variables. Their biases and mean square errors are expressed and simulated. These mean square errors are smaller (the efficiencies are higher) than those of the sample mean estimator and those of other ratio estimators when the correlation between the study and the auxiliary variables exceeds 0.1 in absolute value. In particular, the proposed estimators are more efficient for low correlations between the study and the auxiliary variables. The gain in efficiency reaches a factor of 230.4% on an empirical dataset where the study variable is weakly correlated with each of the two auxiliary variables, and 182.1% on another empirical dataset where it is strongly correlated.
MSC:
| 62D05 | Sampling theory, sample surveys |
References:
| [1] | Abu-Dayyeh, W. A.; Ahmad, M. S.; Ahmad, R. A., Some estimators of a finite population mean using auxiliary information, Applied Mathematics and Computation, 139, 2-3, 287-298 (2003) · Zbl 1019.62008 · doi:10.1016/S0096-3003(02)00180-7 |
| [2] | Amin, M. N.; Hanif, M.; Kadilar, C., Improved exponential type estimators using the information of two auxiliary variables, Middle-East Journal of Scientific Research, 19, 12, 1711-1715 (2014) · doi:10.5829/idosi.mejsr.2014.19.12.1905 |
| [3] | Bahl, S.; Tuteja, R. K., Ratio and product type exponential estimator, Journal of Information & Optimization Sciences, 12, 1, 159-163 (1991) · Zbl 0727.62018 · doi:10.1080/02522667.1991.10699058 |
| [4] | Chand, L., Some Ratio type Estimators based on Two or More Auxiliary Variables. (Unpublished Ph.D. Dissertation) (1975), Iowa: Iowa State University, Iowa |
| [5] | Cochran, W. G., Sampling Techniques (1977), New York: John Wiley and Sons, New York · Zbl 0353.62011 |
| [6] | Guha, S.; Chandra, H., Improved estimation of finite population mean in two-phase sampling with subsampling of the non-respondents, Mathematical Population Studies, 28, 1, 24-44 (2021) · Zbl 1483.62023 · doi:10.1080/08898480.2019.1694325 |
| [7] | Khan, M.; Al-Hossain, A. Y., A note on a difference-type estimator of population mean under two phase sampling design, SpringerPlus, 5, 723 (2016) · doi:10.1186/s40064-016-2368-1 |
| [8] | Koyuncu, N.; Kadilar, C., Ratio and product estimators in stratified random sampling, Journal of Statistics in Planing and Inference, 139, 8, 2552-2558 (2009) · Zbl 1162.62003 · doi:10.1016/j.jspi.2008.11.009 |
| [9] | Koyuncu, N.; Kadilar, C., Family of estimators of population mean using two auxiliary variables in stratified random sampling, Communication in Statistics Theory and Methods, 38, 14, 2398-2417 (2009) · Zbl 1170.62009 · doi:10.1080/03610920802562723 |
| [10] | Lu, J.; Yan, Z.; Aegerter, C. M., A class of ratio estimators of a finite population mean using two auxiliary variables, PLoS ONE, 9, 2, e89538 (2014) · doi:10.1371/journal.pone.0089538 |
| [11] | Misra, S.; Yadav, D. K.; Dipika, Estimation of population mean using auxiliary information in presence of measurement errors, International Journal of Engineering Sciences and Research Technology, 6, 6, 499-502 (2017) · doi:10.5281/zenodo.817860 |
| [12] | Muneer, S.; Khalil, A.; Shabbir, J., A new improved ratio-product type exponential estimator of finite population variance using auxiliary information, Journal of Statistical Computation and Simulation, 88, 16, 3179-3192 (2018) · Zbl 07192710 · doi:10.1080/00949655.2018.1504947 |
| [13] | Muneer, S.; Khalil, A.; Shabbir, J., A parent-generalized family of chain ratio exponential estimators in stratified random sampling using supplementary variables, Communications in Statistics Computation and Simulation (2020) · Zbl 07584575 · doi:10.1080/03610918.2020.1748887 |
| [14] | Murthy, M. N., Sampling Theory and Methods (1967), Calcutta: Statistical Publishing Society, Calcutta · Zbl 0183.20602 |
| [15] | Olkin, I., Multivariate ratio estimation for finite populations, Biometrika, 45, 1-2, 154-165 (1958) · Zbl 0088.12505 · doi:10.1093/biomet/45.1-2.154 |
| [16] | Shabbir, J., Efficient utilization of two auxiliary variables under stratified double sampling, Communication in Statistics Theory and Method, 47, 1, 92-101 (2018) · Zbl 1388.62020 · doi:10.1080/03610926.2017.1300280 |
| [17] | Shabbir, S.; Gupta, J., A new estimator of population mean in stratified sampling, Communications in Statistics - Theory and Methods, 35, 7, 1201-1209 (2006) · Zbl 1107.62012 · doi:10.1080/03610920600629112 |
| [18] | Shabbir, J.; Gupta, S., On estimating finite population mean in simple and stratified random sampling, Communications in Statistics - Theory and Methods, 40, 2, 199-212 (2011) · Zbl 1208.62015 · doi:10.1080/03610920903411259 |
| [19] | Shabbir, J.; Gupta, S., Estimation of finite population mean in simple and stratified random sampling using two auxiliary variables, Communication in Statistics Theory and Methods, 46, 20, 10135-10148 (2017) · Zbl 1380.62040 · doi:10.1080/03610926.2016.1231822 |
| [20] | Shabbir, J.; Gupta, S., Estimation of finite population mean using two auxiliary variables in stratified two phase sampling, Communications in Statistics -Simulation and Computation, 46, 2, 1238-1256 (2017) · Zbl 1362.62022 · doi:10.1080/03610918.2014.995817 |
| [21] | Singh, B. K.; Choudhury, S., Exponential chain ratio and product type estimators for finite population mean under double sampling scheme, Global Journal of Science Frontier Research (F), 12, 6, 1-13 (2012) |
| [22] | Singh, B. K.; Choudhury, S.; Kalita, D., A class of exponential chain ratio-product type estimator with two auxiliary variables under double sampling scheme, Electronic Journal of Applied Statistical Analysis, 6, 2, 166-174 (2013) · doi:10.1285/i20705948v6n2p166 |
| [23] | Singh, G. N.; Khalid, M., An effective estimation strategy for population mean under random non-response situations in two-phase successive sampling, Communication in Statistics Theory and Method, 47, 19, 4641-4660 (2018) · Zbl 1508.62027 · doi:10.1080/03610926.2018.1444179 |
| [24] | Singh, H. P.; Yadav, A.; Pal, S. K., An efficient use of two auxiliary variables in stratified random sampling, International Journal of Agricultural and Statistics Sciences, 14, 2, 739-747 (2018) |
| [25] | Zaman, T., An efficient exponential estimator of the mean under stratified random sampling, Mathematical Population Studies, 28, 2, 104-121 (2021) · Zbl 1483.62040 · doi:10.1080/08898480.2020.1767420 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
