On MDL Estimation for Simple Contaminated Gaussian Location Families

The performance of MDL density estimators defined as 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 non-exponential 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.