Statistics for Mathematicians by Victor M. Panaretos

Statistics for Mathematicians by Victor M. Panaretos

Author:Victor M. Panaretos
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham


such that T is not a constant function. Assume that the parameter space is an open set (recall that, among others, this implies that the function γ(⋅) is twice differentiable). Let be the maximum likelihood estimator of ϕ 0 , assumed to exist. Then,

and

▸ Remark 3.24 (Non-Degeneracy)

To say that a distribution is non-degenerate (as the theorem requires) means that it does not assign probability 1 to a single value .

Proof (Proof of Theorem 3.23)

Under the conditions of the Theorem, Proposition 3.21 (p. 75) implies that the MLE is unique for all n. Furthermore, Proposition 2.​11 (p. 51) implies that



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