{"title":"Mathematical Programming on Multivariate Calibration Estimation in Stratified Sampling","authors":"Dinesh Rao, M.G.M. Khan, Sabiha Khan","volume":72,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1623,"pagesEnd":1628,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10096","abstract":"Calibration estimation is a method of adjusting the\noriginal design weights to improve the survey estimates by using\nauxiliary information such as the known population total (or mean)\nof the auxiliary variables. A calibration estimator uses calibrated\nweights that are determined to minimize a given distance measure to\nthe original design weights while satisfying a set of constraints\nrelated to the auxiliary information. In this paper, we propose a new\nmultivariate calibration estimator for the population mean in the\nstratified sampling design, which incorporates information available\nfor more than one auxiliary variable. The problem of determining the\noptimum calibrated weights is formulated as a Mathematical\nProgramming Problem (MPP) that is solved using the Lagrange\nmultiplier technique.","references":"[1] Briedt, F.J. and Opsomer, J.D. (2000). Local polynomial regression\nestimators in survey sampling. Ann. Statist., 28, 1026-1053.\n[2] Chen, J. and Qin, J. (1993). Empirical likelihood estimation for finite\npopulations and the effective usage of auxiliary information. Biometrika\n80, 107-116.\n[3] Deville, J.C. and S\u251c\u00f1rndal, C.E. (1992). Calibration estimators in survey\nsampling. J. Amer. Statist. Assoc., 87, 376-382.\n[4] J.-M. Kim, E.A. Sungur, and T.-Y. Heo (2007), \"Calibration Approach\nEstimators in Stratified Sampling\", Statistics & Probability Letters; Vol.\n77, 1, 99-103.\n[5] Kim, J.K. (2009). Calibration estimation using empirical likelihood in\nunequal probability sampling. Statist. Sinica., 19, 145-157.\n[6] Singh, S. (2003). Advanced Sampling Theory with Applications.\nDordrecht: Kluwer Academic Publishers.\n[7] Singh, S., Horn, S., Yu, F. (1998). Estimation of variance of the general\nregression estimator: higher level calibration approach. Survey\nMethodology 24, 41-50.\n[8] Wu, C. & Sitter, R.R. (2001). A model-calibration approach to using\ncomplete auxiliary information from survey data. J. Amer. Statist.\nAssoc., 96, 185-193.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 72, 2012"}