# Does increasing the sample size always increase the accuracy of a consistent estimator?

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

Research output: Book/ReportReportAcademic

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## Abstract

Birnbaum (1948) introduced the notion of peakedness about \theta of a random variable T, defined by $P(| T - \theta | <\epsilon), \epsilon > 0$. What seems to be not well-known is that, for a consistent estimator Tn 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 interquartile range are presented.
Original language English Eindhoven Eurandom 5 Published - 1999

### Publication series

Name Report Eurandom 99007 1389-2355

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