An improved regression type estimator to estimate population mean under non-normality in simple random sampling

Abstract

In sample survey, the auxiliary information correlated with the study variable is utilized in the ratio method of estimation to increase the efficiencies of estimators when the regression line y on x is linear and passes through origin. But, it is not always possible that the regression line y on x should pass through origin. In this situation, the regression method of estimation is more appropriate method of estimation. Under this method of estimation, the correlation between study variable and auxiliary variables is either highly positive or negative. In this paper, we study the classical regression estimator using robust modified maximum likelihood estimator (MMLE) and the properties have been provided theoretically.

In the paper, we specifically concentrate on the condition where the error term is non-normal. We derive the mean square error of the proposed estimator and obtain the conditions for which the proposed estimator has less mean square error than the classical regression estimator. Also, the theoretical results with simulations under several super population models have been supported and the robustness property of the proposed estimator has been studied. We illustrate that modified maximum likelihood estimates for estimating finite population mean provide robust estimate under non-normality or when some other common data anomalies such as outliers exist.

Keywords:

• Regression estimator
• Modified maximum likelihood
• Robust linear regression
• Super population
• Simulation study
• Simple random sampling