Outlier detection in a preliminary test estimator of the mean

Pre-test estimator has earlier been introduced to estimate the mean of a normal distribution when non-sample prior information is available. In this paper, our aim is to consider the pre-test estimator for the mean in the presence of outliers. A well known procedure to define the pre-test estimator of the mean is based on the sample mean. However, the sample mean is not a robust location estimator. In order to overcome this problem, we replace it by M-location estimators. In particular, we use the M-location estimators obtained from Huber [6], Hampel[3] and Tukey [12]. Also, we use the median as an alternative location estimator. Cook's squared distance (Cook [2]) is used to study the influential observations in a Monte Carlo study. We conduct a simulation study to illustrate the performance of the pre-test estimator of the mean in the presence of outliers in the data.