A Dual Problem of Calibration Ratio-Type Estimator under Stratified Systematic Sampling Scheme

Document Type : Original Article

Authors
Alka Singh 1
Piyush Rai 2
Muhammad Qasim 3
1 Department of Mathematics and Statistics, Banasthali University, Rajasthan, India.
2 Department of Statistics, Banaras Hindu University, Varanasi, India.
3 Department of Economics, Finance and Statistics, Jonkoping University, Sweden.\
10.22034/jirss.2024.1999153.1017
Abstract
This article introduces a dual problem of widely used calibration ratio-type estimators for estimating population mean of the study variable considering auxiliary information under dual constraints using stratified systematic sampling design. Under large sample approximations, the expression for bias and variance of the proposed estimator are derived. In addition, the optimality condition for the proposed estimator and hence optimum variance expression is also obtained for the same. Moreover, a study based on real-life data is carried out to judge the performance of the proposed calibration estimator in terms of minimum relative bias and relative root mean squared error criterion. The study reveals that the calibration ratio-type estimator under dual constraints may be preferred in practice as it provides consistent and more precise parameter estimates.
Keywords
Auxiliary Information
Calibration Estimation
Ratio-type Estimator
Systematic Sampling
Subjects
Alka, Rai, P.K., and M. Qasim. (2019). Two-step calibration of design weights under two auxiliary variables in sample survey. Journal of Statistical Computation and Simulation, 89(12),2316–2327.
 
Alka, Ekpenyong, E.J., Rai, P.K, and Tiwari, S. (2021). Calibration estimator of population mean under stratified systematic sampling design. International Journal of Agricultural and Statistical Sciences, 17, 2353–61.
 
Choudhury, S. and Singh, B. K. (2012a). An Efficient Class of Dual to Product-cum-Dual to Ratio Estimators of Finite Population Mean in Sample Surveys. Global Journal of Science Frontier Research Mathematics & Decision Sciences, 12(3): Version 1.0. ISSN: 2249–4626.
 
Choudhury, S. and Singh, B. K. (2012b). A Class of Chain ratio-cum-dual to Ratio Type Estimator with Two Auxiliary Characters under Double Sampling in Sample Surveys. Statistics in Transition- New Series, 13(1), 65–78.
 
Clement, E. P. and Enang, E. I. (2017). On the Efficiency of Ratio Estimator over the Regression Estimator. Communications in Statistics-Theory and Methods, 46 (11), 5357-5367.
 
Cochran,W. G. (1977). Sampling Techniques, 3rd edition, John Wiley, New York.
 
Clement, E. P., Udofia, G. A. and Enang, E. I. (2014). Sample design for domain calibration estimators. International Journal of Probability and Statistics, 3(1), 8-14.
 
Clement, E. P. and Enang, E. I. (2015). Calibration approach alternative ratio estimator for population mean in stratified sampling. International Journal of Statistics and Economics, 16(1), 83-93.
 
Deville, J. C. and Sarndal, C. E. (1992). Calibration Estimators in Survey Sampling. Journal of the American Statistical Association, 87, 376-382.
 
Estevao, V. M. and Sarndal, C. E. (2006). Survey estimates by calibration on complex auxiliary information. International Statistical Review, 74, 127-147.
 
Etuk, S. I., Enang, E. I. and Ekpenyong, E. J. (2016).AModified Class of Ratio Estimators for Population Mean. Communications in Statistics -Theory andMethods, 45(4), 837-849.
 
Kim, J. K. and Park, M. (2010). Calibration Estimation in Survey Sampling. International Statistical Review, 78(1), 21-29.
 
Koyuncu, N. and Kadilar, C. (2013). Calibration Estimators Using Different Measures in Stratified Random Sampling. International Journal of Modern Engineering Research, 3(1), 415-419.
 
Koyuncu, N. and Kadilar, C. (2016). Calibration weighting in stratified random sampling. Communications in Statistics-Simulation and Computation, 45(7), 2267-2275.
 
Onyeka, A.C. (2012). Estimation of Population Mean in Post-Stratified Sampling using Known Value of Some Population Parameter(s). Statistics in Transition-New Series, 13(1), 65–78.
 
Onyeka, A.C. (2013). Dual to Ratio Estimators of Population Mean in Post-Stratified Sampling usingKnownValue of Some Population Parameters. Global Journal of Science Frontier Research Mathematics & Decision Sciences, 13(2), Version 1.0. ISSN: 2249-4626.
 
Ozgul, N. (2019). New calibration estimator based on two auxiliary variables in stratified sampling. Communications in Statistics-Theory and Methods, 48(6), 1481-1492.
 
Rai, P. K., Tiwari, S.,&Alka. (2024). Calibration approach-based estimator of population total under successive sampling design. Communications in Statistics - Theory and Methods, 1–15.
 
Sarndal, C. E. (2007). The Calibration Approach in Survey Theory and Practice. Survey Methodology, 33, 99-119.
 
Singh, S. (2013) A Dual Problem of Calibration of Design Weights, Statistics, 47(3), 566-574.
Singh, H. P., Rathour, A. and Solanki, R. S. (2012). An Improved Dual to Chain Ratio Type Estimator for the Population Mean. J. Stat, 1(3), 1–6.
 
Singh, R., Chauhan, P., Sawan, N. and Smarandache, F. (2009). Improvement in Estimating
the Population Mean using Exponential Estimator in Simple Random Sampling. Bulletin of Statistics & Economics, 3(9), 13–18.
 
Singh, R., Chauhan, P., Sawan, N. and Smarandache, F. (2011). Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables. Italian Journal of Pure and Applied Mathematics, 28, 101–108.
 
Solanki, R. S., Singh, H. P. and Rathour, A. (2012): An Alternative Estimator for Estimating the Finite Population Mean Using Auxiliary Information in Sample Surveys. ISRN Probability and Statistics Article ID 657682, doi:10.5402/2012/657682.
 
Zaman, T., and Bulut, H. (2023). Robust calibration for estimating the population mean using stratified random sampling. Scientia Iranica, DOI: 0.24200/SCI.2023.59408.6224.
Journal of the Iranian Statistical Society
Volume 23, Issue 1
June 2024
Pages 117-130

  • Receive Date 28 March 2023
  • Revise Date 24 November 2023
  • Accept Date 02 August 2024