Abstract | ||
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The minimum message length principle is an information theoretic criterion that links data compression with statistical inference. This paper studies the strict minimum message length (SMML) estimator for $d$-dimensional exponential families with continuous sufficient statistics, for all $d \ge 1$. The partition of an SMML estimator is shown to consist of convex polytopes (i.e. convex polygons when $d=2$) which can be described explicitly in terms of the assertions and coding probabilities. While this result is known, we give a new proof based on the calculus of variations, and this approach gives some interesting new inequalities for SMML estimators. We also use this result to construct an SMML estimator for a $2$-dimensional normal random variable with known variance and a normal prior on its mean. |
Year | Venue | Field |
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2013 | CoRR | Discrete mathematics,Mathematical optimization,Minimum message length,Normal distribution,Exponential family,Regular polygon,Polytope,Statistical inference,Sufficient statistic,Mathematics,Estimator |
DocType | Volume | Citations |
Journal | abs/1302.0581 | 0 |
PageRank | References | Authors |
0.34 | 2 | 1 |
Name | Order | Citations | PageRank |
---|---|---|---|
James G. Dowty | 1 | 1 | 2.04 |