Performance of robust confidence intervals for estimating population mean under both non-normality and in presence of outliers

Abstract

We proposed two robust confidence interval estimators, namely, the median interquartile range confidence interval (MDIQR) and the trimean interquartile range confidence interval (TRIQR) for the population mean (μ) as an alternative to the classical confidence interval. The proposed methods are based on the asymptotic normal theorem (ANT) for the sample median (MD) and the sample trimean (TR). We compare the performance of the proposed interval estimators with the classical estimators by using a simulation study through the following criteria: (i) average width (AW) and (ii) empirical coverage probability (CP). It is evident from simulation study is that the proposed robust interval estimator performs well under both criterion and when the observations are sampled from contaminated normal distribution. However, when the observations are sampled from non-normal distributions, the classical confidence interval performs the best in the shorter width sense, but the coverage probability tends to be smaller than the two proposed robust confidence interval estimators for all sample sizes. For illustration purposes, two real life data sets are analyzed, which supported the findings of the simulation study to some extent.