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On the uniqueness of the M. L. estimates in curved exponential families. (English) Zbl 0657.62031
Curved families [cf. B. Efron, Ann. Stat. 6, 362-376 (1978; Zbl 0436.62027)] 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 beta- distribution. Generalized curved exponential families are considered as well.

62F10 Point estimation
62J02 General nonlinear regression
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