A note on some translation-parameter families of densities for which the median is an M.L.E.

Rao, C. R. ; Ghosh, J. K. (1971) A note on some translation-parameter families of densities for which the median is an M.L.E. Sankhya Series A, 33 . pp. 91-92. ISSN 0581-572x

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Abstract

The following theorem is proved in the forthcoming book by Kagan, Linnik, and Rao: If the median is an m.l.e. of θ for a sample of the size n=4 from a population with density f(x-θ ) and f(x) is lower semi-continuous at the origin then f(x)=ke-α|x| , -∞ <x<∞ , α>0. The object of this note is to show that the theorem is false if we require the median is an m.l.e. of θ for samples of size n=2 and 3.

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