Expected Absolute Error of the Usual Estimator of the Binomial Parameter

Abstract For X with binomial (n, p) distribution the usual measure of the error of X/n as an estimator of p is its standard error Sn(p) = √{E(X/n – p)2} = √{p(1 – p)/n}. A somewhat more natural measure is the average absolute error Dn(p) = E‖X/n – p‖. This article considers use of Dn(p) instead of Sn(p) in a student's first introduction to statistical estimation. Exact and asymptotic values of Dn(p), and the appearance of its graph, are described in detail. The same is done for the Poisson distribution.