Abstract
The maximum quasi-likelihood method suggested by Wedderburn (1974) is widely used. The quasi-score equation (QSE) is linear with respect to a random variable and has useful properties in practical analysis. However, for some variance functions, there are no probability models that match the quasi-likelihood in the univariate 1-parameter family. Consequently, QSE can not be derived by differentiating the likelihood by the mean parameter and it loses the interpretation. In this paper, a tilted exponential family is introduced and new interpretation is given to QSE via the tilted exponential family under the above conditions.
