Robust Estimation by Means of Scaled Bregman Power Distances. Part I. Non-homogeneous Data

摘要

In contemporary data analytics, one often models uncertainty-prone data as samples stemming from a sequence of independent random variables whose distributions are non-identical but linked by a common (scalar or multidimensional) parameter. For such a context, we present in the current Part I a new robustness-featured parameter-estimation framework, in terms of minimization of the scaled Bregman power distances of Stummer and Vajda [23] (see also [21]); this leads to a wide range of outlier-robust alternatives to the omnipresent (non-robust) method of maximum-likelihood-examination, and extends the corresponding method of Ghosh and Basu [7]. In Part II (see [20]), we provide some applications of our framework to data from potentially rare but dangerous events described by approximate extreme value distributions.