Mathematical Programming on Multivariate Calibration Estimation in Stratified Sampling
Calibration estimation is a method of adjusting the
original design weights to improve the survey estimates by using
auxiliary information such as the known population total (or mean)
of the auxiliary variables. A calibration estimator uses calibrated
weights that are determined to minimize a given distance measure to
the original design weights while satisfying a set of constraints
related to the auxiliary information. In this paper, we propose a new
multivariate calibration estimator for the population mean in the
stratified sampling design, which incorporates information available
for more than one auxiliary variable. The problem of determining the
optimum calibrated weights is formulated as a Mathematical
Programming Problem (MPP) that is solved using the Lagrange
multiplier technique.
[1] Briedt, F.J. and Opsomer, J.D. (2000). Local polynomial regression
estimators in survey sampling. Ann. Statist., 28, 1026-1053.
[2] Chen, J. and Qin, J. (1993). Empirical likelihood estimation for finite
populations and the effective usage of auxiliary information. Biometrika
80, 107-116.
[3] Deville, J.C. and Särndal, C.E. (1992). Calibration estimators in survey
sampling. J. Amer. Statist. Assoc., 87, 376-382.
[4] J.-M. Kim, E.A. Sungur, and T.-Y. Heo (2007), "Calibration Approach
Estimators in Stratified Sampling", Statistics & Probability Letters; Vol.
77, 1, 99-103.
[5] Kim, J.K. (2009). Calibration estimation using empirical likelihood in
unequal probability sampling. Statist. Sinica., 19, 145-157.
[6] Singh, S. (2003). Advanced Sampling Theory with Applications.
Dordrecht: Kluwer Academic Publishers.
[7] Singh, S., Horn, S., Yu, F. (1998). Estimation of variance of the general
regression estimator: higher level calibration approach. Survey
Methodology 24, 41-50.
[8] Wu, C. & Sitter, R.R. (2001). A model-calibration approach to using
complete auxiliary information from survey data. J. Amer. Statist.
Assoc., 96, 185-193.
[1] Briedt, F.J. and Opsomer, J.D. (2000). Local polynomial regression
estimators in survey sampling. Ann. Statist., 28, 1026-1053.
[2] Chen, J. and Qin, J. (1993). Empirical likelihood estimation for finite
populations and the effective usage of auxiliary information. Biometrika
80, 107-116.
[3] Deville, J.C. and Särndal, C.E. (1992). Calibration estimators in survey
sampling. J. Amer. Statist. Assoc., 87, 376-382.
[4] J.-M. Kim, E.A. Sungur, and T.-Y. Heo (2007), "Calibration Approach
Estimators in Stratified Sampling", Statistics & Probability Letters; Vol.
77, 1, 99-103.
[5] Kim, J.K. (2009). Calibration estimation using empirical likelihood in
unequal probability sampling. Statist. Sinica., 19, 145-157.
[6] Singh, S. (2003). Advanced Sampling Theory with Applications.
Dordrecht: Kluwer Academic Publishers.
[7] Singh, S., Horn, S., Yu, F. (1998). Estimation of variance of the general
regression estimator: higher level calibration approach. Survey
Methodology 24, 41-50.
[8] Wu, C. & Sitter, R.R. (2001). A model-calibration approach to using
complete auxiliary information from survey data. J. Amer. Statist.
Assoc., 96, 185-193.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59159", author = "Dinesh Rao and M.G.M. Khan and Sabiha Khan", title = "Mathematical Programming on Multivariate Calibration Estimation in Stratified Sampling", abstract = "Calibration estimation is a method of adjusting the
original design weights to improve the survey estimates by using
auxiliary information such as the known population total (or mean)
of the auxiliary variables. A calibration estimator uses calibrated
weights that are determined to minimize a given distance measure to
the original design weights while satisfying a set of constraints
related to the auxiliary information. In this paper, we propose a new
multivariate calibration estimator for the population mean in the
stratified sampling design, which incorporates information available
for more than one auxiliary variable. The problem of determining the
optimum calibrated weights is formulated as a Mathematical
Programming Problem (MPP) that is solved using the Lagrange
multiplier technique.", keywords = "Calibration estimation, Stratified sampling,
Multivariate auxiliary information, Mathematical programming
problem, Lagrange multiplier technique.", volume = "6", number = "12", pages = "1738-5", }