No. 999

Title:

Robust parameter estimation with a small bias against heavy contamination

Author(s):

Fujisawa, Hironori (The Institute of Statistical Mathematics);
Eguchi, Shinto (The Institute of Statistical Mathematics)

Key words:

Cross entropy; Divergence; Invariance; Pythagorian rela

Abstract:

    The robust parameter estimation is defined as the minimization of a certain cross entropy. It is shown that the bias can become sufficiently small even in the case of heavy contamination. It is also illustrated that the robust parameter estimation is derived from a kind of projection, which is a geometric interpretation based on a Pythagorian relation. An iterative algorithm is constructed to obtain the robust estimator from the viewpoint of the triangular relation among three density functions. It is seen that the asymptotic variance of the robust estimator under contamination is almost proportional to that under no contamination, according to the ratio of contamination. We see that the contamination is naturally ignored. These properties are proved without the help of conventional indexes of robustness