D. R. Bickel, submitted to InterStat. 1 ROBUST AND EFFICIENT ESTIMATION OF THE MODE OF CONTINUOUS DATA: THE MODE AS A VIABLE MEASURE OF CENTRAL TENDENCY

Key words: Robust estimation; robust mode; mode estimator; average value; measure of location; asymmetry; transformation; efficiency. ABSTRACT. Although a natural measure of the central tendency of a sample of continuous data is its mode (the most probable value), the mean and median are the most popular measures of location due to their simplicity and ease of estimation. The median is often used instead of the mean for asymmetric data because it is closer to the mode and is insensitive to extreme values in the sample. However, the mode itself can be reliably estimated by first transforming the data into approximately normal data by raising the values to a real power, and then estimating the mean and standard deviation of the transformed data. With this method, two estimators of the mode of the original data are proposed: a simple estimator based on estimating the mean by the sample mean and the standard deviation by the sample standard deviation, and a more robust estimator based on estimating the mean by the median and the standard deviation by the standardized median absolute deviation