A new robust ratio estimator with reference to non-normal distribution

Abstract

In this study, we have observed some situations in which modified maximum likelihood estimation becomes inappropriate to develop the robust and efficient estimator of the population mean. To cope with these situations, an alternative methodology known as the generalized least squares estimation based on order statistics is suggested. Integrating the generalized least squares estimation to usual ratio estimator, a new robust ratio estimator for estimating the finite population mean in simple random sampling assuming a long-tailed symmetric distribution is proposed. The efficiency and robustness of the proposed estimator are compared with the usual ratio estimator and the robust ratio estimator due to Oral and Oral. The mean square error and relative efficiency are computed through the simulation study to compare performance of the estimators with each other using various contamination models. Further, a real life example is provided to show the performance and the implementation of proposed estimator.

Keywords:

• Generalized least square estimator
• modified maximum likelihood estimator
• new robust ratio estimator
• mean square error

Acknowledgment

The authors are thankful to the anonymous referees for their helpful comments that improved the initial version of this article which led to the discovery of many new things.