  This paper focuses on the Bregman divergence defined by the reciprocal
function, called the inverse divergence. For the loss function defined by the
monotonically increasing function $f$ and inverse divergence, the conditions
for the statistical model and function $f$ under which the estimating equation
is unbiased are clarified. Specifically, we characterize two types of
statistical models, an inverse Gaussian type and a mixture of generalized
inverse Gaussian type distributions, to show that the conditions for the
function $f$ are different for each model. We also define Bregman divergence as
a linear sum over the dimensions of the inverse divergence and extend the
results to the multi-dimensional case.
