Iterative Mid-Range with Application to Estimation Performance Evaluation

If a data set has a large range (e.g., the large elements are several orders of magnitude greater than the small elements), then the median is usually applied to measure its central tendency. However, it has two drawbacks. A novel measure of central tendency called iterative mid-range (IMR) is proposed. It has several attractive properties and can overcome the drawbacks of the median. Estimation performance is often evaluated in a statistical sense by the Monte Carlo method. Given a set of estimation errors, estimation performance is evaluated by measures of central tendency of error, that is, by finding a typical value (e.g., root-mean-square error) to represent the errors. The proposed IMR is applied to estimation performance evaluation, and it is named IMR error (IMRE). This letter advocates replacing the median by our proposed IMR in many cases.