  We discuss unbiased estimation equations in a class of objective function
using a monotonically increasing function $f$ and Bregman divergence. The
choice of the function $f$ gives desirable properties such as robustness
against outliers. In order to obtain unbiased estimation equations,
analytically intractable integrals are generally required as bias correction
terms. In this study, we clarify the combination of Bregman divergence,
statistical model, and function $f$ in which the bias correction term vanishes.
Focusing on Mahalanobis and Itakura-Saito distances, we provide a
generalization of fundamental existing results and characterize a class of
distributions of positive reals with a scale parameter, which includes the
gamma distribution as a special case. We discuss the possibility of latent bias
minimization when the proportion of outliers is large, which is induced by the
extinction of the bias correction term.
