A New Estimator: Median of the Distribution of the Mean in Robustness

Abstract

In some statistical methods, the statistical information is provided in terms of the values used by classical estimators, such as the sample mean and sample variance. These estimations are used in a second stage, usually in a classical manner, to be combined into a single value, as a weighted mean. Moreover, in many applied studies, the results are given in these terms, i.e., as summary data. In all of these cases, the individual observations are unknown; therefore, computing the usual robustness estimators with them to replace classical non-robust estimations by robust ones is not possible. In this paper, the use of the median of the distribution Fx¯ of the sample mean is proposed, assuming a location-scale contaminated normal model, where the parameters of Fx¯ are estimated with the classical estimations provided in the first stage. The estimator so defined is called median of the distribution of the mean, MdM. This new estimator is applied in Mendelian randomization, defining the new robust inverse weighted estimator, RIVW.