On the uniqueness of the M. L. estimates in curved exponential families
Andrej Pázman · Czech digital mathematics library · 1986
ANDREJ PAZMANCurved families (cf.Efron [3]) imbedded in exponential families having full rank differentiable sufficient statistics are considered.It is proved that if the rank is less or equal to the dimension of the sample space, then the maximum likelihood estimate is unique.Examples: the gaussian nonlinear regression, the gaussian family with unknown mean and variance, the ^-distribution.Generalized curved exponential families are considered as well.