2022/07/25 by Andrey Akinshin, Akinshin, Andrey
Computer Science · Mathematics · #62G05 #62G35 #62Q05 #Advanced Statistical Methods and Models #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2207.12005
openalex publication_date 2022/07/25 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
The median absolute deviation is a widely used robust measure of statistical dispersion. Using a scale constant, we can use it as an asymptotically consistent estimator for the standard deviation under normality. For finite samples, the scale constant should be corrected in order to obtain an unbiased estimator. The bias-correction factor depends on the sample size and the median estimator. When we use the traditional sample median, the factor values are well known, but this approach does not provide optimal statistical efficiency. In this paper, we present the bias-correction factors for the median absolute deviation based on the Harrell-Davis quantile estimator and its trimmed modification which allow us to achieve better statistical efficiency of the standard deviation estimations. The obtained estimators are especially useful for samples with a small number of elements.