Estimation of Mean in Single-phase Sampling with High and Low Extreme Maximum values using auxiliary information

Abstract

Significant improvement has been introduced to regression-in-ratio estimators in simple random sampling. However, such improvement will be jeopardized when there is extreme maximum or minimum value in survey data. This study has proposed three improved regression-in-ratio estimators that would correct the over-estimation or under-estimation effect as a result of extreme maximum or minimum values in survey data, respectively. The bias and the mean square error expressions were established for comparison of the proposed estimators. Theoretical comparison and empirical comparison, through simulation for twenty six populations with high and low extreme maximum values, confirmed that the proposed estimators were, generally, efficient over the reviewed estimators. Though, the proposed estimators were less bias to the reviewed estimators, but they were confirmed to be asymptotically efficient. Suggestion for further study in the detection of significant extreme values in sample survey data was proposed.