No. 1000

Title:

On a class of robust parameter estimation against heavy contamination

Author(s):

Fujisawa, Hironori (The Institute of Statistical Mathematics)

Key words:

Bias; Characterization; Cross entropy; Divergence; Invariance; Pythagorian relation.

Abstract:

    This paper focuses on the robust parameter estimation based on a cross entropy and illustrates some conditions where the robust parameter estimation works well even in the case of heavy contamination. Such conditions essentially consist of three parts: (i) The cross entropy is empirically estimable to make it easy to estimate the parameter. (ii) The contamination is automatically ignored to remove the effect of contamination in parameter estimation. (iii) The bias can become sufficiently small for any ratio of contamination. It is shown under these conditions that the cross entropy suitable for robust parameter estimation even in the case of heavy contamination is essentially unique.