Geodesic
On limiting towards the boundaries of exponential families
Kybernetika, Tome 51 (2015) no. 5, pp. 725-738
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This work studies the standard exponential families of probability measures on Euclidean spaces that have finite supports. In such a family parameterized by means, the mean is supposed to move along a segment inside the convex support towards an endpoint on the boundary of the support. Limit behavior of several quantities related to the exponential family is described explicitly. In particular, the variance functions and information divergences are studied around the boundary.
This work studies the standard exponential families of probability measures on Euclidean spaces that have finite supports. In such a family parameterized by means, the mean is supposed to move along a segment inside the convex support towards an endpoint on the boundary of the support. Limit behavior of several quantities related to the exponential family is described explicitly. In particular, the variance functions and information divergences are studied around the boundary.
DOI : 10.14736/kyb-2015-5-0725
Classification : 60A10, 62B10, 94A17
Keywords: exponential family; variance function; Kullback–Leibler divergence; relative entropy; information divergence; mean parametrization; convex support 
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Matúš, František. On limiting towards the boundaries of exponential families. Kybernetika, Tome 51 (2015) no. 5, pp. 725-738. doi: 10.14736/kyb-2015-5-0725

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