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SMML estimators for 1-dimensional continuous data

Information Theory 2012-12-21 v1 math.IT Statistics Theory Machine Learning Statistics Theory

Abstract

A method is given for calculating the strict minimum message length (SMML) estimator for 1-dimensional exponential families with continuous sufficient statistics. A set of nn equations are found that the nn cut-points of the SMML estimator must satisfy. These equations can be solved using Newton's method and this approach is used to produce new results and to replicate results that C. S. Wallace obtained using his boundary rules for the SMML estimator. A rigorous proof is also given that, despite being composed of step functions, the posterior probability corresponding to the SMML estimator is a continuous function of the data.

Cite

@article{arxiv.1212.4906,
  title  = {SMML estimators for 1-dimensional continuous data},
  author = {James G. Dowty},
  journal= {arXiv preprint arXiv:1212.4906},
  year   = {2012}
}

Comments

10 pages, 2 tables and 1 figure

R2 v1 2026-06-21T22:57:42.381Z