A New Robust Confidence Interval for the Population Mean µ based on Winsorized Modified One Step M-Estimator and Winsorized Standard Deviation

In this paper, we propose a new confidence interval (CI) for the population mean µ based on robust estimators, which involves the application of the winsorized modified one-step M-estimator (WMOM) and winsorized standard deviation (WSD). The proposed method is modified for the Student's t confidence interval CI under the non-normal distribution. The performances of the proposed confidence interval were evaluated via a Monte-Carlo simulation study by considering the coverage ratio (CR) and the average length (AL) as performance criteria. The simulation study results show the superior performance of the proposed confidence interval (CI) over the classical parametric Student's t for data from a non-normal distribution. Two real data sets were analyzed, and the results agree to some extent with those of the simulation study. The results confirm the suitability of the proposed CI estimator for both normally and non-normally distributed data.