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28 March 2024 |
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Article overview
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Fisher Information of Scale | Peter Ruckdeschel
; Helmut Rieder
; | Date: |
6 May 2010 | Abstract: | We define Fisher information of scale of any distribution function F on the
real line by
I_{sca}(F):= sup (integral x phi’(x) F(dx))^2 / (integral phi^2(x) F(dx)),
phi in C_{c1}
where C_{c1} denotes the set of differentiable functions with continuous
derivative of compact support and, by convention, 0/0:=0. I_{sca}(F) is weakly
lower semicontinuous and convex. I_{sca}(F) is finite iff the usual assumptions
on densities hold, under which Fisher information of scale is classically
defined, and then both notions agree. Finiteness of I_{sca}(F) is also
equivalent to L_2-differentiability and local asymptotic normality,
respectively, in the parameter of the induced scale model
F_sigma(x)=F(x/sigma), sigma>0. | Source: | arXiv, 1005.0983 | Services: | Forum | Review | PDF | Favorites |
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