# Entropic Projections and Dominating Points

ESAIM: Probability and Statistics (2010)

- Volume: 14, page 343-381
- ISSN: 1292-8100

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topLéonard, Christian. "Entropic Projections and Dominating Points." ESAIM: Probability and Statistics 14 (2010): 343-381. <http://eudml.org/doc/250830>.

@article{Léonard2010,

abstract = {
Entropic projections and dominating points are solutions to convex
minimization problems related to conditional laws of large
numbers. They appear in many areas of applied mathematics such as
statistical physics, information theory, mathematical statistics,
ill-posed inverse problems or large deviation theory. By means of convex conjugate
duality and functional analysis, criteria are derived for the
existence of entropic projections, generalized entropic
projections and dominating points. Representations of the
generalized entropic projections are obtained. It is shown that
they are the “measure component" of the solutions to some
extended entropy minimization problem. This approach leads to new
results and offers a unifying point of view. It also permits to
extend previous results on the subject by removing unnecessary
topological restrictions. As a by-product, new proofs of already
known results are provided.
},

author = {Léonard, Christian},

journal = {ESAIM: Probability and Statistics},

keywords = {Conditional laws of large numbers; random measures;
large deviations; entropy; convex optimization; entropic projections; dominating points; Orlicz spaces; laws of large numbers; large deviations},

language = {eng},

month = {12},

pages = {343-381},

publisher = {EDP Sciences},

title = {Entropic Projections and Dominating Points},

url = {http://eudml.org/doc/250830},

volume = {14},

year = {2010},

}

TY - JOUR

AU - Léonard, Christian

TI - Entropic Projections and Dominating Points

JO - ESAIM: Probability and Statistics

DA - 2010/12//

PB - EDP Sciences

VL - 14

SP - 343

EP - 381

AB -
Entropic projections and dominating points are solutions to convex
minimization problems related to conditional laws of large
numbers. They appear in many areas of applied mathematics such as
statistical physics, information theory, mathematical statistics,
ill-posed inverse problems or large deviation theory. By means of convex conjugate
duality and functional analysis, criteria are derived for the
existence of entropic projections, generalized entropic
projections and dominating points. Representations of the
generalized entropic projections are obtained. It is shown that
they are the “measure component" of the solutions to some
extended entropy minimization problem. This approach leads to new
results and offers a unifying point of view. It also permits to
extend previous results on the subject by removing unnecessary
topological restrictions. As a by-product, new proofs of already
known results are provided.

LA - eng

KW - Conditional laws of large numbers; random measures;
large deviations; entropy; convex optimization; entropic projections; dominating points; Orlicz spaces; laws of large numbers; large deviations

UR - http://eudml.org/doc/250830

ER -

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