Efficient estimation of population variance in sample surveys utilizing auxiliary information
Housila P. Singhhpsujn@gmail.comSchool of Studies in StatisticsVikram UniversityUjjain, Madhya Pradesh, 456010, IndiaView full profile → , *Neha GargCorresponding authorneha1garg@gmail.comSchool of SciencesIndira Gandhi National Open UniversityNew Delhi, Delhi, 110068, IndiaView full profile → , Anant Patelanantpatel880@gmail.comSchool of SciencesIndira Gandhi National Open UniversityNew Delhi, Delhi, 110068, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 02 Jun 2025
- Published Online:
- 22 May 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JSMS-1577
- Pages:
- 715–741
Abstract
This paper addresses the issue of estimating population variance by incorporating auxiliary information within the framework of a simple random sampling without a replacement scheme. We have suggested classes of estimators for population variance (S2y) of the study variable (Y) utilizing information available on the population variance (S2x) of the auxiliary variable (X). Expressions for the bias and mean squared error (MSE) for the suggested estimators up to the first order of approximation have been obtained. Furthermore, we have established optimal conditions under which these new estimators outperform certain existing ones. An empirical study using three real population datasets has been conducted to substantiate the theoretical results.
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References
[1] S. Singh, S. Horn, and F. Yu, “Estimation of variance of the regression estimator: Higher level calibration approach”, Survey Methodology, vol. 24, pp. 41-50 (1998).
[2] U. Daraz, and M. Khan, “Estimation of variance of the difference-cum-ratio-type exponential estimator in simple random sampling,” RMS: Research in Mathematics & Statistics, vol. 8, no. 1, 1899402 (2021).
[3] U. Daraz, M. A. Alomair, O. Albalawi, A. S. Al Naim, “New techniques for estimating finite population variance using ranks of Auxiliary Variable in Two-Stage Sampling,” Mathematics, vol. 12, no. 17, 2741 (2024a).
[4] U. Daraz, M. A. Alomair, and O. Albalawi, “Variance estimation under some transformation for both symmetric and asymmetric data”. Symmetry, vol. 16, no. 8, 957 (2024b).
[5] A. K. Das and T. P. Tripathi, “Use of auxiliary information in estimating the finite population variance,” Sankhya C, vol. 40, pp. 139-148 (1978).
[6] S. Gupta and J. Shabbir, “Variance estimation in simple random sampling using auxiliary information,” Hacettepe Journal of Mathematics and Statistics, vol. 37, no. 1, pp. 57-67 (2008).
[7] C. T. Isaki, “Variance estimation using auxiliary information,” Journal of the American Statistical Association, vol. 78, no. 381, pp. 117-123 (1983).
[8] A. Kumar and A. S. Siddiqui, “Enhanced estimation of population mean using simple random sampling,” Research in Statistics, vol. 2, no. 1, 2335949 (2024).
[9] M. Kumar, R. Singh, N. Sawan, and P. Chauhan, “Exponential ratio method of estimation in the presence of measurement errors,” International Journal of Agricultural and Statistical Sciences, vol. 7, no. 2, pp. 457-461 (2011).
[10] P. Mishra, A. Sharma, N. K. Adichwal, S. Rai, and R. Singh, “Log-product-type estimator for estimation of population variance using auxiliary information,” Thailand Statistician, vol. 22, no. 3, pp. 610-617 (2024).
[11] P. Sharma and R. Singh, “Improved dual to variance ratio type estimators for population variance,” Chilean Journal of Statistics, vol. 5, no. 2, pp. 45-54 (2014).
[12] S. Singh, Advanced sampling theory with applications: how Michael ‘Selected’ Amy, Kluwer Academic Publishers, The Netherlands, (2003).
[13] H. P. Singh, “A note on the estimation of variance of sample mean using the knowledge of coefficient of variation in normal population,” Communications in Statistics-Theory and Methods, vol. 15, no. 12, pp. 3737-3746 (1986).
[14] H. P. Singh and R. S. Solanki, “A new procedure for variance estimation in simple random sampling using auxiliary information,” Statistical Papers, vol. 54, pp. 479-497 (2013).
[15] H. Singh, and P. Chandra, “An alternative to ratio estimator of the population variance in sample surveys,” Statistics in Transition, vol. 9, pp. 89-103 (2008).
[16] L. N. Upadhyaya and H. P. Singh, “Use of transformed auxiliary variable in estimating the finite population mean,” Biometrical Journal: Journal of Mathematical Methods in Biosciences, vol. 41, no. 5, pp. 627-636 (1999a).
[17] S. A. Mahmud, S. K. Pal, and H. P. Singh, “An innovative approach to factor-type exponential estimation using auxiliary information,” Journal of Information and Optimization Sciences, vol. 45, no. 7, pp. 2057–2070 (2024), DOI: 10.47974/JIOS-1755.
[18] S. K. Yadav and C. Kadilar, “Improved exponential type ratio estimator of population variance,” Revista colombiana de Estadistica, vol. 36, no. 1, pp. 145-152 (2013).
[19] S. K. Yadav, C. Kadilar, J. Shabbir, and S. Gupta, “Improved family of estimators of population variance in simple random sampling,” Journal of Statistical Theory and Practice, vol. 9, pp. 219-226 (2015).
