Summary
2020
Session Number:E01
Session:
Number:E01-4
On MDL Estimation for Simple Contaminated Gaussian Location Families
K. Miyamoto, Junichi Takeuchi,
pp.587-591
Publication Date:2020/10/18
Online ISSN:2188-5079
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Summary:
The performance of MDL density estimators definedas the minimizer of two part code lengths is guaranteed in
terms of the redundancy of the two part code [2], [3]. When
the true density belongs to the assumed model, the redundancy
of a code can be bounded by the regret (pointwise redundancy)
of the code. Then, the construction of two part codes which
achieve small regret based on quantization of parametric family
is developed. For exponential families, it is known that we
can achieve sufficiently small regret by using this construction
[4]. For non-exponential families, the evaluation of the regret
achieved by using this construction breaks. However, for nonexponential
families under certain assumptions, by enhancing
this construction using local exponentially family bundles [1], we
can design efficient two part codes [9]. In this paper, we show
that we can apply this coding method to contamination model
[5] with simple settings and give the guarantee of performance
of MDL estimators for them.