# Sample size and the accuracy of a consistent estimator

P. Laan, van der, C. Eeden, van

Birnbaum (1948) introduced the notion of peakedness about () of a random variable T, defined by $P ( IT - \thetaI <\epsilon), \epsilon > 0$. What seems to be not well-known is that, for a consistent estimator T_n of \theta, its peakedness does not necessarily converge to 1 monotonically in n. In this article some known results on how the peakedness of the sample mean behaves as a function of n are recalled. Also, new results concerning the peakedness of the median and the midrange are presented.