|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Fisher Information in Group-Type Models | | Peter Ruckdeschel
; | | Date: |
6 May 2010 | | Abstract: | In proofs of L_2-differentiability, Lebesgue densities of a central
distribution are often assumed right from the beginning. Generalizing Theorem
4.2 of Huber[81], we show that in the class of smooth parametric group models
these densities are in fact consequences of a finite Fisher information of the
model, provided a suitable representation of the latter is used. The proof uses
the notions of absolute continuity in k dimensions and weak differentiability.
As examples to which this theorem applies, we spell out a number of models
including a correlation model and the general multivariate location and scale
model. As a consequence of this approach, we show that in the (multivariate)
location scale model, finiteness of Fisher information as defined here is in
fact equivalent to L_2-differentiability and to a log-likelihood expansion
giving local asymptotic normality of the model. Paralleling Huber’s proofs for
existence and uniqueness of a minimizer of Fisher information to our situation,
we get existence of a minimizer in any weakly closed set of central
distributions F. If, additionally to analogue assumptions to those of
Huber[81], a certain identifiability condition for the transformation holds, we
obtain uniqueness of the minimizer. This identifiability condition is satisfied
in the multivariate location scale model. | | Source: | arXiv, 1005.1027 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER