Advancing Sampling Techniques: Multivariate Ratio Estimation for Variance Vector in Two-Phase Sampling
DOI:
https://doi.org/10.61506/01.00056Keywords:
variance-covariance matrix, two-phase sampling, bias, ratio estimator, multi-auxiliary variables, simulationAbstract
The problem of variance vector estimation using multi-auxiliary variables is not quite often considered in the literature. In the present study, we propose a multivariate ratio estimation approach for estimating a vector of variances in two-phase sampling using a vector of variables, following the situation if the desired parameters are available only for some of the auxiliary variables. Some special cases of the proposed generalized multivariate variance estimator have also been discussed. Expressions of the bias, and generalized variance has been derived. With the help of real-life data, the applicability of the proposed multivariate variance estimator has been given, and it is shown that the proposed multivariate estimator is more efficient than the modified versions of multivariate variance estimators. A simulation study has also been carried out to show that the proposed estimator surpasses the modified version of multivariate estimators.
References
Abu-Dayyeh, W. and Ahmed, M.S. (2002). General Estimator for a finite population variance using multivariate auxiliary variable. Journal of Statistical Theory and Applications, 1(2), 143-147.
Ahmed, M.S., Raman, M.S., and Hossain, M.I., (2000). Some competitive estimators of finite population variance Multivariate Auxiliary Information. Information and Management Sciences. 11 (1), 49-54.
Ahmad, Z., Hussain I. and Hanif, M., (2016). Estimation of Finite Population Variance in Successive Sampling Using Multi-Auxiliary Variables. Communication in Statistics- Theory and Methods. 45 (3), 553-565. DOI: https://doi.org/10.1080/03610926.2013.833236
Asghar, A., Sanaullah, A. and Hanif, M., (2014). Generalized exponential type estimator for population variance in survey sampling. Revista Colombiana de Estadística, 37 (1), 213-224. DOI: https://doi.org/10.15446/rce.v37n1.44368
Abid, M., Ahmed, S., Tahir, M., Zafar Nazir, H., & Riaz, M., (2019). Improved ratio estimators of variance based on robust measures. Scientia Iranica, 26(4), 2484-2494.
Cekim, O., H., Kadilar, C. (2020). ln-Type Variance Estimators in Simple Random Sampling. Pakistan Journal of Statistics and Operation Research, 689-696. DOI: https://doi.org/10.18187/pjsor.v16i4.3072
Naz, F. A. R. A. H., Abid, M., Nawaz, T., & Pang, T., (2020). Enhancing efficiency of ratio-type estimators of population variance by a combination of information on robust location measures. Scientia Iranica, 27(4), 2040-2056.
Niaz, I., Sanaullah, A., Saleem, I., & Shabbir, J., (2022). An improved efficient class of estimators for the population variance. Concurrency and Computation: Practice and Experience, 34(4), e6620. DOI: https://doi.org/10.1002/cpe.6620
Das, A.K. and Tripathi, T.P., (1978). Use of auxiliary information in estimating the finite population variance. Sankhya, 40, 139-148.
David Robinson (2016). broom: Convert Statistical Analysis Objects into Tidy Data Frames. R package version 0.4.1.
Graunt, J., (1662). Natural and political observations upon the Bill of Mortality London: John Martyn.
Haq, A, Usman, M., Khan, M., (2021). Estimation of finite population variance under stratified random sampling. Communications in Statistics - Simulation and Computation, 1-17. DOI: https://doi.org/10.1080/03610918.2021.2009866
Hadley Wickham (2016). tidyverse: Easily Install and Load 'Tidyverse' Packages. R package version 1.0.0. CRAN.R-project.org/package=tidyverse.
Isaki, C., (1983). Variance estimation using auxiliary information. Journal of the American Statistical Association, 78, 117-123. DOI: https://doi.org/10.1080/01621459.1983.10477939
Kadilar, C., Cingi, H., (2006). Improvement in variance using auxiliary Information}, Hecettepe Journal of Mathematics and Statistics, 35 (1), 111-115.
Kim, J.K., Sitter, R.R., (2003). Efficient variance estimation for two-phase sampling. Statistic Sinica, 13, 641-653, 2003.
Olufadi, Y. and Kadilar, C., (2014). A study on the chain ratio type estimator of finite population variance. Journal of Probability and Statistics. DOI: https://doi.org/10.1155/2014/723982
Olkin, I., (1958). Multivariate ratio estimation for finite populations. Biometrika, 45, 154-165. DOI: https://doi.org/10.1093/biomet/45.1-2.154
Singh, H. P., Singh, S., Kim, J. M. (2003). Variance estimation using multiauxiliary information for random non-response in survey sampling. Statistica, 63 (1), 23-40.
Singh H. P., Chandra P., Singh S., (2010). Efficient use of auxiliary variables in estimating finite population variance in two-phase sampling. Communications for Statistical Applications and Methods, 17 (2), 165-181. DOI: https://doi.org/10.5351/CKSS.2010.17.2.165
Singh, H. P., Solanki, R. S., (2013). A new procedure for variance estimation in simple random sampling using auxiliary information. Statistical Papers, 54 (2), 479-497. DOI: https://doi.org/10.1007/s00362-012-0445-2
Singh, R., Singh, V. K., (2015). Improved Class of Estimators for Variance under Single and Two-Phase Sampling. Journal of Statistics Applications and Probability, 4 (1), 161-165.
Sanaullah, A., Hanif, M. Asghar, A., (2016). Generalized Exponential Estimators for Population Variance under Two-Phase. International Journal of Applied Computational Mathematics, 2 (1), 75-84, 2016. DOI: https://doi.org/10.1007/s40819-015-0047-5
Singh, H.P., Pal, S.K., (2016). Improved estimation of finite population variance using auxiliary information in presence of measurement error. Revista Investigacion Operacional, 37 (2), 147-162.
Ismail, M., Kanwal, N., Shahbaz, M. Q., (2018). Generalized ratio-product-type estimator for variance using auxiliary information in simple random sampling, Kuwait Journal of Science, 45 (1), 79-88.
Upadhyaya, L. N., Singh, H. P., (1999). An estimator for population variance that utilizes the kurtosis of an auxiliary variable in sample surveys. Vikram Mathemat, 19, 4-17.
Daraz, U., Khan, M., (2021). Estimation of variance of the difference-cum-ratio-type exponential estimator in simple random sampling. RMS: Research in Mathematics & Statistics, 8(1), 1899402. DOI: https://doi.org/10.1080/27658449.2021.1899402
Yadav, S.K., Kumar, R., Kumar, S., Verma, S., Kumar, S., (2015). Efficient Estimator of Population Variance Using of Coefficient of Kurtosis and Population Mean of Auxiliary Variable. International Journal of Mathematics and its Application, 3 (4), 85-91.
Zaman, T., Bulut, H., (2021). An efficient family of robust-type estimators for the population variance in simple and stratified random sampling. Communications in Statistics-Theory and Methods, 1-15. DOI: https://doi.org/10.1080/03610926.2021.1955388
