Chiang Mai Journal of Science

 The purpose of this study is to propose estimators of the population total and the population mean using a model-assisted approach in inverse simple random sampling with and without replacement. It was found that the proposed estimators are biased, so the mean squared errors of the proposed estimators were investigated. The precision of the estimators is compared with those of the unbiased estimators given by Greco and Naddeo [2]. The simulation results indicate that the absolute relative biases of the proposed estimators decrease when the correlation between X, the auxiliary or independent variable and Y, the study variable increase. The absolute relative biases are small for all situations. As for the mean squared error estimates of the model-assisted estimate of the population total and the variance estimates of the unbiased estimate, it can be seen for sampling both with and without replacement that if the population prevalence increases then the variance estimates and the mean squared errors increase. They also decrease when the value of m, the number of units satisfying specified conditions in the samples increases. At low correlation between the auxiliary variable X and the study variable Y, the model-assisted estimator is as efficient as the unbiased estimator, whereas at high correlation between X and Y, the model-assisted estimator is considerably more efficient than the unbiased estimator.