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 by a linear sum over the dimensions of the inverse divergence and extend the results to the multi-dimensional case.