A Class of Simple Linear Estimators of the Standard Deviation of the Normal Distribution

Abstract

A class of simple linear estimators of the standard deviation of the normal distribution is considered. They are based on the differences between the sums of the observations in the tails of the ordered sample. For normal distributions they are asymptotically unbiased and possess good efficiency—even for small samples. Also for a wide range of non-normal distributions they are reasonably robust asymptotically.