Naïve Family of Estimators for Population Mean Using Auxiliary Parameters in Survey Sampling

Abstract

In order to estimate the population, mean of a study variable under a straightforward random sampling without replacement framework, this paper presents a naive broad family of ratio estimators that make use of a variety of auxiliary measures. The study looks at particular instances that include auxiliary data like the median, quartile deviation, and coefficient of variation. A first-order approximation is maintained for the introduced estimators' bias and Mean Square Error (MSE). Furthermore, real-world data is used to validate the performance of the introduced estimators, and theoretical conditions are supplied for comparing their efficiency with those of existing estimators. The suggested estimators are more effective than other ratio-based estimators, as shown by numerical analysis, making them suitable for use in a variety of real-world situations.