The strong consistency for maximum likelihood estimates: a proof not based on the likelihood ratio

Fiorin, Silvano

doi:10.1016/s0764-4442(00)01718-3

Cited by 3 publications

(2 citation statements)

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“…Although the latter claimed that the underlying assumptions are easy to check in practice, a few of them involve the calculation of upper bounds which are not obvious to obtain. Although Wald's proof of consistency has opened the way for more studies on the strong consistency of the MLE (see for example [3,5,7]), it remains a central result in Statistics. When the MLE is available in closed-form, the study of its strong consistency could certainly be done directly by using its closed-form expression and the properties of the underlying statistical distribution.…”

Section: Introductionmentioning

confidence: 99%

Existence, uniqueness and strong consistency of the maximum likelihood estimator for a model of accidents frequencies

Geraldo

2023

GJOM

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The aim of this paper is to prove the existence, uniqueness and strong consistency (i.e. almost sure convergence to the true unknown value) of the maximum likelihood estimator (MLE) of the vector parameter for a statistical model used in statistics applied to road safety. In the general case, the strong consistency of the MLE may be established by using the well-known result by Abraham Wald (in 1949) or its variants under a set of conditions. However, for the model considered in this paper, all these conditions are very difficult to verify because of the great dimension of the parameter space and the rather complex expression of the log-likelihood function. To circumvent these difficulties, we first demonstrate that the MLE exists and is unique afterwards we demonstrate the strong consistency of the MLE using the properties of the model and some theorems of mathematical analysis.

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Section: Introductionmentioning

confidence: 99%

Existence, uniqueness and strong consistency of the maximum likelihood estimator for a model of accidents frequencies

Geraldo

2023

GJOM

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“…We do not make use of any Uniform Law of Large Numbers. Our method does not belong to the Glivenko-Cantelli approaches of consistency, as in [Dud98], [Fio00], [AK94], [vdV98] and [vdG03, vdG00] and references therein.…”

Section: Introductionmentioning

confidence: 99%