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 |
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Place of Publication | Eindhoven |
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Publisher | Eurandom |
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Number of pages | 5 |
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Publication status | Published - 1999 |
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Name | Report Eurandom |
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Volume | 99007 |
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ISSN (Print) | 1389-2355 |
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