Parametrizations of Non-Linear Models
文献中提出了多种模型参数化方法，追求极大似然估计的方差稳定性、正态似然、渐近无偏性和零渐近偏度。本文在一维弯曲指数族中找到了对应参数化，它们属于一类由微分方程刻画的变换，在非线性正态回归模型中这些变换相同。
summary in the literature there have been many suggestions on how to parametrize models. some properties you can seek are (1) stability of variance of the mle; (2) normal likelihood; (3) zero asymptotic skewness of the mle; (4) asymptotic unbiasedness of the mle. the parametrizations corresponding to these demands are found in the one-dimensional curved exponential family. they all belong to a general class of transformations, but they are in general not identical. the transformations in this class are characterized by a differential equation. the transformations are identical in the nonlinear normal regression model.