Reference : When the score function is the identity function - A tale of characterizations of the...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/51307
When the score function is the identity function - A tale of characterizations of the normal distribution
English
Ley, Christophe mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
19-Nov-2020
Econometrics and Statistics
Yes
[en] Maximum likelihood characterization ; Score function ; Skew-symmetric distributions ; Stein characterization ; Variance bounds
[en] The normal distribution is well-known for several results that it is the only to fulfil. Much less well-known is the fact that many of these characterizations follow from the fact that the derivative of the log-density of the normal distribution is the (negative) identity function. This a priori very simple yet surprising observation allows a deeper understanding of existing characterizations and paves the way for an immediate extension of various seemingly normal-based characterizations to a general density by replacing the (negative) identity function in these results with the derivative of that log-density.
http://hdl.handle.net/10993/51307
https://doi.org/10.1016/j.ecosta.2020.10.001

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