Adroit family of estimators of population mean using known auxiliary parameters. (English) Zbl 07750626
Summary: This article introduces an upgraded family of dual estimators for the population mean of main variable using some known supplementary information. To construct the family of estimators, a suitable transformation on the study variable as well as auxiliary variable has been used. The sampling features of the proposed class of estimators have been studied up to first order under large sample approximation. Several existing estimators have been observed and found as particular members of the proposed family of estimators. The optimum values of the characterizing scalars of the suggested family of estimators are obtained through the method of maxima-minima. The least value of the Mean Squared Error (MSE) of the proposed class of estimators is also obtained for these optimal values of the characterizing constants. The proposed family of estimators is compared theoretically with the other competing estimators of population mean. To judge the performance of the suggested family of estimators over others, numerical illustration has also been given. The estimator with minimum MSE is recommended for practical utility in different areas of applications. The results show the suggested estimator performs better than the competing estimators, therefore it may be used in different applications.
MSC:
| 62D05 | Sampling theory, sample surveys |
| 62-XX | Statistics |
| 62F10 | Point estimation |
| 62J05 | Linear regression; mixed models |
| 62G35 | Nonparametric robustness |
Keywords:
study variable; auxiliary variable; ratio estimator; product estimator; bias; mean squared error (MSE)References:
| [1] | Cochran, W. G., The estimation of the yields of cereal experiments by sampling for the ratio gain to total produce, J. Agric. Sci., 30, 262-275 (1940) |
| [2] | Robson, D. S., Applications of multivariate polykays to the theory of unbiased ratio type estimation, J. Amer. Statist. Assoc., 52, 511-522 (1957) · Zbl 0078.33504 |
| [3] | Murthy, M. N., Product method of estimation, Sankhya, A, 26, 69-74 (1964) · Zbl 0138.13002 |
| [4] | Srivastava, S. K., An estimator using auxiliary information in sample surveys, Calcutta Statist. Assoc. Bull., 16, 121-132 (1967) |
| [5] | Walsh, J. E., Generalization of ratio estimate for population total, Sankhya, A, 32, 99-106 (1970) · Zbl 0203.51201 |
| [6] | Gupta, P. C., On some quadratic and higher degree ratio and product estimators, J. Indian Soc. Agricultural Statist., 30, 2, 71-80 (1978) |
| [7] | Mohanty, S.; Das, H. N., Use of transformation in sampling, J. Indian Soc. Agricultural Statist., 23, 83-87 (1971) |
| [8] | Sen, A. R., Estimation of the population mean when the coefficient of variation is known, Commun. Stat. Theory Methods A, 7, 657-672 (1978) · Zbl 0391.62022 |
| [9] | Bandyopadhyay, S., Improved ratio and product estimators, Sankhya, 42, 45-49 (1980) · Zbl 0486.62013 |
| [10] | Srivenkataramana, T., A dual to ratio estimator in sample surveys, Biometrika, 67, 199-2040 (1980) · Zbl 0426.62008 |
| [11] | Srivenkataramana, T.; Tracy, D. S., An alternative to ratio method in sample survey, Ann. Inst. Statist. Math., 32, 111-120 (1980) · Zbl 0456.62010 |
| [12] | Srivenkataramana, T.; Tracy, D. S., On positive and negative valued auxiliary in survey sampling, Current Sci., 55, 13 (1984) |
| [13] | Pandey, G. S., Product-cum-power estimators, Calcutta Statist. Assoc. Bull., 29, 103-108 (1980) · Zbl 0446.62015 |
| [14] | Sahai, A.; Ray, S. K., An efficient estimator using auxiliary information, Metrika, 27, 271-275 (1980) · Zbl 0449.62007 |
| [15] | Singh, H. P.; Upadhyaya, L. N., A dual to modified ratio estimator using coefficient of variation of auxiliary variable, Proc. Natl. Acad. Sci. India, 56, A, 4, 336-340 (1986) · Zbl 0668.62009 |
| [16] | Mohanty, S.; Sahoo, L. N., A class of estimators based on mean per unit and ratio estimators, Statistica, anno XLVII, 3, 473-477 (1987) · Zbl 0718.62014 |
| [17] | Singh, G. N., On the improvement of product method of estimation in sample surveys, J. Indian Soc. Agricultural Statist., 56, 3, 267-275 (2003) · Zbl 1188.62073 |
| [18] | Singh, H. P.; Tailor, R., Use of known correlation coefficient in estimating the finite population mean, Stat. Transition, 6, 4, 553-560 (2003) |
| [19] | Singh, H. P.; Ruiz-Espejo, M., On linear regression and ratio-product estimation of a finite population mean, Statistician, 52, 1, 59-67 (2003) |
| [20] | Singh, H. P.; Tailor, R., Estimation of finite population mean with known coefficient of variation of an auxiliary character, Statistica, anno LXV, 3, 407-418 (2005) · Zbl 1188.62078 |
| [21] | Singh, H. P.; Tailor, R.; Tailor, R., Duals to Mohanty and Sahoo’s estimators, Statistica, anno LXVIII, 34, 1-23 (2008) · Zbl 1453.62319 |
| [22] | Singh, H. P.; Agnihotri, N., A general procedure of estimating population mean using auxiliary information in sample surveys, Stat. Transition-New Ser., 9, 1, 71-87 (2008) |
| [23] | Misra, G. C.; Shukla, A. K.; Yadav, S. K., A comparison of regression methods for improved estimations in sampling, J. Reliab. Stat. Stud., 2, 2, 85-90 (2009) · Zbl 1247.62172 |
| [24] | Sharma, B.; Tailor, R., A new ratio-cum-dual to ratio estimator of finite population mean in simple random sampling, Glob. J. Sci. Front. Res., 10, 1, 27-31 (2010) |
| [25] | Misra, G. C.; Yadav, S. K.; Shukla, A. K., A class of regression type estimators in survey sampling, Stat. Transition-New Ser., 12, 3, 579-586 (2011) |
| [26] | Upadhyaya, L. N.; Singh, H. P.; Chatterjee, S.; Yadav, R., A generalized family of transformed ratio-product estimators of finite population mean in sample surveys, Model Assist. Stat. Appl., 6, 2, 137-150 (2011) |
| [27] | Upadhyaya, L. N.; Singh, H. P.; Chatterjee, S.; Yadav, R., Improved ratio and product exponential type estimators, J. Stat. Theory Pract., 5, 2, 285-302 (2011) · Zbl 1458.62053 |
| [28] | Yadav, R.; Upadhyaya, L. N.; Singh, H. P.; Chatterjee, S., Almost unbiased ratio and product type exponential estimators, Stat. Transition, 13, 3, 537-550 (2012) |
| [29] | Chaudhary, S.; Singh, B. K., An efficient class of dual to product-cum-dual to ratio estimator of finite population mean in sample surveys, Glob. J. Sci. Front. Res., 12, 3, 25-33 (2012) |
| [30] | Yadav, S. K.; Kadilar, C., Efficient family of exponential estimator for population mean, Hacet. J. Math. Stat., 42, 6, 671-677 (2013) · Zbl 1296.62024 |
| [31] | Yadav, S. K.; Mishra, S. S., Developing improved predictive estimator for finite population mean using auxiliary information, Statistika, 95, 1, 76-85 (2015) |
| [32] | Singh, H. P.; Pal, S. K.; Mehta, V., A generalized class of ratio-cum-dual to ratio estimators of finite population mean using auxiliary information in sample surveys, Math. Sci. Lett., 5, 2, 203-211 (2016) |
| [33] | Yadav, S. K.; Misra, S.; Mishra, S. S.; Shukla, A. K.; Chaudhary, N. K., Efficient estimation of population mean using non-conventional measures of dispersion of auxiliary variable, Int. J. Agric. Stat. Sci., 12, 2, 547-553 (2016) |
| [34] | Yadav, S. K.; Pandey, H., A new difference type median based estimator of the finite population mean, Int. J. Agric. Stat. Sci., 13, 1, 289-295 (2017) |
| [35] | Yadav, R., An efficient dual to ratio-cum-product estimator for the population mean in stratified random sampling, Int. J. Sci. Res. Math. Stat. Sci., 5, 2, 13-20 (2018) |
| [36] | Zatezalo, T.; Gupta, S.; Yadav, S. K.; Shabbir, J., Assessing the adequacy of first order approximations in ratio type estimators, J. Interdiscip. Math., 21, 6, 1395-1411 (2018) |
| [37] | Hussain, I.; Haq, A., A new family of estimators for population mean with dual use of the auxiliary information, J. Stat. Theory Pract., 13, 23 (2019) · Zbl 1426.62028 |
| [38] | Singh, L.; Yadav, S. K.; Mishra, S. S., A new efficient estimator for the population mean, Int. J. Agric. Stat. Sci., 14, 2, 671-677 (2018) |
| [39] | Yadav, S. K.; Dixit, M. K.; Dhungana, H. N.; Mishra, S. S., Improved estimators for estimating average yield using auxiliary variable, Int. J. Math. Eng. Manag. Sci., 4, 5, 1228-1238 (2019) |
| [40] | Baghel, S.; Yadav, S. K., Restructured class of estimators for population mean using an auxiliary variable under simple random sampling scheme, J. Appl. Math. Stat. Inform., 16, 1, 61-75 (2020) · Zbl 1524.62029 |
| [41] | Irfan, M.; Javed, M.; Bhatti, S. H.; Raza, M. A.; Ahmad, T., Almost unbiased optimum estimators for population mean using dual auxiliary information, J. King Saud Univ. Sci., 32, 6, 2835-2844 (2020) |
| [42] | Singh, H. P.; Nigam, P., A general class of dual to ratio estimator, Pak. J. Stat. Oper. Res., 16, 3, 421-431 (2020) |
| [43] | Shahzad, U.; Hanif, M.; Sajjad, I.; Anas, M. M., Quantile regression-ratio-type estimators for mean estimation under complete and partial auxiliary information, Sci. Iran., 29, 3, 1705-1715 (2020) |
| [44] | Grover, L. K.; Kaur, A., An improved regression type estimator of population mean with two auxiliary variables and its variant using robust regression method, J. Comput. Appl. Math., 382, Article 113072 pp. (2021) · Zbl 1448.62026 |
| [45] | N. Thongsak, N. Lawson, Classes of Dual to Modified Ratio Estimators for Estimating Population Mean in Simple Random Sampling, in: Research, Invention, and Innovation Congress: Innovation Electricals and Electronics, RI2C, 2021, pp. 211-215. |
| [46] | Shahzad, U.; Al-Noor, N. H.; Hanif, M.; Sajjad, I., An exponential family of median based estimators for mean estimation with simple random sampling scheme, Comm. Statist. Theory Methods, 50, 20, 4890-4899 (2021) · Zbl 07532178 |
| [47] | Yadav, S. K.; Zaman, T., Use of some conventional and non-conventional parameters for improving the efficiency of ratio-type estimators, J. Stat. Manag. Syst. (2021) |
| [48] | Singh, D.; Yadav, R., A modified three parameters family of estimators for population mean in sample surveys, Int. J. Agric. Stat. Sci., 17, Supplement 1, 2027-2032 (2021) |
| [49] | Singh, D.; Yadav, R.; Chandra, H., An improved ratio-product-ratio class of estimators for estimating finite population mean, Int. J. Agric. Stat. Sci., 17, 1, 119-123 (2021) |
| [50] | Zaman, T.; Kadilar, C., New class of exponential estimators for finite population mean in two-phase sampling, Comm. Statist. Theory Methods, 50, 4, 874-889 (2021) · Zbl 07532926 |
| [51] | Zaman, T., An efficient exponential estimator of the mean under stratified random sampling, Math. Popul. Stud., 28, 2, 104-121 (2021) · Zbl 1483.62040 |
| [52] | Zaman, T.; Kadilar, C., Exponential ratio and product type estimators of the mean in stratified two-phase sampling, AIMS Math., 6, 5, 4265-4279 (2021) · Zbl 1484.62022 |
| [53] | Bhushan, S.; Kumar, A., Predictive estimation approach using difference and ratio type estimators in ranked set sampling, J. Comput. Appl. Math., 410, Article 114214 pp. (2022) · Zbl 1493.62045 |
| [54] | Sharma, D. K.; Yadav, S. K., Optimal generalized searls estimation procedure of population mean under ranked set sampling scheme, Int. J. Math. Oper. Res., 21, 3, 305-320 (2022) |
| [55] | Yadav, S. K., Modified searls predictive estimation of population mean using known auxiliary character, Thail. Stat., 20, 1, 53-65 (2022) · Zbl 1486.62025 |
| [56] | Shahzad, U.; Ahmad, I.; Almanjahie, I. M.; Al-Omari, A. I., Three-fold utilization of supplementary information for mean estimation under median ranked set sampling scheme, PLoS One, 17, 10, Article e0276514 pp. (2022) |
| [57] | Vishwakarma, G. K.; Yadav, S. K.; Bari, T., Generalized difference-cum exponential class of estimators for estimating population parameters of the sensitive variable, Math. Probl. Eng. (2022) |
| [58] | Yadav, S. K.; Smarandache, F., Generalized neutrosophic sampling strategy for elevated estimation of population mean, Neutrosophic Sets and Syst., 53, 219-238 (2023) |
| [59] | Chaubey, Y. P.; Singh, M.; Dwivedi, T. D., A note on an optimality property of the regression estimator, Biometrika J., 26, 4, 465-467 (1984) |
| [60] | Kadilar, C.; Cingi, H., Improvement in estimating the population mean in simple random sampling, Appl. Math. Lett., 19, 75-79 (2006) · Zbl 1125.62002 |
| [61] | Tailor, R.; Sharma, B. K., A modified ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis, Stat. Transition-New Ser., 10, 1, 15-24 (2009) |
| [62] | Murthy, M. N., Sampling Theory and Methods (1967), statistical publishing society: statistical publishing society Calcutta · Zbl 0183.20602 |
| [63] | Sukhatme, P. V.; Sukhatme, B. V., Sampling Theory of Surveys with Applications (1970), Iowa State University Press: Iowa State University Press Ames, U.S.A · Zbl 0239.62008 |
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