Electronic Resource
Springer
Annals of the Institute of Statistical Mathematics
43 (1991), S. 515-537
ISSN:
1572-9052
Keywords:
Divergence
;
contrast functional
;
yoke
;
minimum divergence estimator
;
geometric estimator
;
curvature
;
dual geometries
;
statistical manifold
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Amari's ±1-divergences and geometries provide an important description of statistical inference. The ±1-divergences are constructed so that they are compatible with a metric that is defined by the Fisher information. In many cases, the ±1-divergences are but two in a family of divergences, called the f-divergences, that are compatible with the metric. We study the geometries induced by these divergences. Minimizing the f-divergence provides geometric estimators that are naturally described using certain curvatures. These curvatures are related to asymptotic bias and efficiency loss. Under special but important restrictions, the geometry of f-divergence is closely related to the α-geometry, Amari's extension of the ±1-geometries. One application of these results is illustrated in an example.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00053370
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