Parametrizations of Non-Linear Models
Philip Hougaard · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1982
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.