Calibration Weighting in Stratified Random Sampling

Abstract

A new calibration estimator is proposed to estimate the population mean in the stratified random sampling. The corrected expression of Tracy et al. (2003) calibrated weights are presented and new improved calibration weights are introduced. Theoretical variance of the suggested estimator is discussed. Also a simulation study is carried out to show the properties of the proposed estimator.

A Goal Programming Approach for Generalized Calibration Weights Estimation in Stratified Random Sampling

“…Motivated by Singh [3] and Tracy [4], Koyuncu and Khadilar [8] proposed their calibration estimator. They also minimized the chi-square distance function subject to three constraints which are the same as the constraints proposed in [3] and in [4].…”

“…But they considered using them at one optimization problem simultaneously. Accordingly it can be stated that they minimized (3.1) subject to the three constraints expressed in (3.2), (3.3) and (3.4) together simultaneously [8].…”

“…Further, Rao [9] proposed a MCE for the population mean in SRS using different constraints. They also suggested minimizing (3.1) as their objective function subject to the same three constraints used in [8] but in case of multi-auxiliary variables.…”

Generalized Class Of Estimators For Population Median Using Auxiliary Information

“…It has been well recognised that use of auxiliary information results in efficient estimators of population parameters. Initially, estimation of median without auxiliary variable analyzed, after that some authors including [6], [9], [24] and [7] used the auxiliary information in median estimation. [6], proposed the problem of estimating the population median M y of study variable Y using the auxiliary variable X for the unites in the sample and its median M x for the whole population.…”

“…Among the proposed estimators t m and t j mq (j=1,2,...9) the performance of the estimator t m ,which is equal efficient to the estimatorM (due to [19]) , is best in the sense of having the least MSE followed by the estimatorM (7) mq which utilize the information on population median M x and ρ c…”