An alternative item sum technique for improved estimators of population mean in sensitive surveys

Abstract

The item sum technique (IST) was developed for the measurement of quantitative sensitive variables. This method is closely related to the unmatched count technique (UCT), which was developed to measure the proportion of dichotomous sensitive items in a human population surveys. In this article, firstly, we proposed an improved IST which has a fruitful advantage that it does not require two subsamples as in usual IST and there is also no need of finding optimum subsample sizes. We derived the mean and variance of the proposed estimator and compare it with the usual IST both theoretically and numerically. Secondly, we suggest some alternative family of estimators of the population mean of sensitive variable and compare them with estimator, based on the proposed one sample version of IST. Thirdly, we utilize auxiliary information in estimation of population mean, say µs of sensitive variable. It is established that the estimator based on the proposed IST is always more efficient than its usual counterpart. The estimator using second raw moment of the auxiliary variable is observed to be more efficient than the other auxiliary information based estimators, namely, the ratio, product and regression estimators. The usual and proposed ISTs are applied to estimate the average number of classes missed by the student during the last semester at the Quaid-i-Azam University. Estimated average of number of missed classes and 95% confidence intervals are reported showing that the proposed IST yields precise estimates compared to the usual IST.