Consistency of Maximum Likelihood and Bayes Estimates

Strasser, Helmut

doi:10.1214/aos/1176345590

Cited by 36 publications

(26 citation statements)

References 4 publications

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“…(1) tl~oO Pfanzagl (1969) and later Perlman (1972), Strasser (1981) and others considered minimum contrast estimators and asymptotically minimum contrast estimators based on i.i.d, data. For such data these estimators can be defined using a simple concept of contrast function.…”

Section: Conditions Equivalent With Consistency Of All Amce'smentioning

confidence: 99%

“…Vajda (1993) considered the general observations and found a condition equivalent with the usual (non-strong) consistency of all AMLE's. He also found an example where the condition of Strasser (1981) is not satisfied but the MLE exists and is strongly consistent. For some observation models he derived a condition doubly equivalent with consistency of all AMCE's (it is equivalent with consistency, and its contrary is equivalent with inconsistency of all AMCE's).…”

Section: Introductionmentioning

confidence: 99%

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Necessary and sufficient conditions for consistency of generalizedM-estimates

Liese

Vajda

1995

Metrika

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Section: Conditions Equivalent With Consistency Of All Amce'smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Necessary and sufficient conditions for consistency of generalizedM-estimates

Liese

Vajda

1995

Metrika

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“…It is known that for fixed prior, the posterior will asymptotically concentrate on the true parameter (Strasser, 1981) generating the data and the scaled posterior will be asymptotically normal (LeCam, 1958;Walker, 1969). Intuitively, with the fixed prior replaced by the AIP, these properties will be kept but with faster rate.…”

Section: Resultsmentioning

confidence: 99%

“…Denote Q m (·|X n ) for the posterior distribution/measure of the density q m (θ|X n ), and P θ the probability measure corresponding to f (·|θ). We list the following conditions, in which the first six are used in Strasser (1981).…”

Section: Resultsmentioning

confidence: 99%

Asymptotically Informative Prior for Bayesian Analysis

Yuan

Gooijer

2014

Communications in Statistics - Theory and Methods

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractIn classical Bayesian inference the prior is treated as fixed, it is asymptotically negligible, thus any information contained in the prior is ignored from the asymptotic first order result. However, in practice often an informative prior is summarized from previous similar or the same kind of studies, which contains non-negligible information for the current study. Here, different from traditional Bayesian point of view, we treat such prior to be non-fixed. In particular, we give the data sizes used in previous studies for the prior the same status as the size of the current dataset, viewing both sample sizes as increasing to infinity in the asymptotic study. Thus the prior is asymptotically non-negligible, and its original effects are ressumed under this view. Consequently, Bayesian inference using such prior is more efficient, as it should be, than that regarded under the existing setting. We study some basic properties of Bayesian estimators using such priors under convex losses and the 0-1 loss, and illustrate the method by an example via simulation.

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“…One of the implications of the main result parallels Strasser (1981). Strasser showed that any set of conditions that gives consistency of the MLE also gives concentration of the posterior.…”

Section: Introductionmentioning

confidence: 80%

Asymptotic normality of the posterior given a statistic

Yuan

Clarke

2004

Can J Statistics

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Abstract:The authors establish the asymptotic normality and determine the limiting variance of the posterior density for a multivariate parameter, given the value of a consistent and asymptotically Gaussian statistic satisfying a uniform local central limit theorem. Their proof is given in the continuous case but generalizes to lattice-valued random variables. It hinges on a uniform Edgeworth expansion used to control the behaviour of the conditioning statistic. They provide examples and show how their result can help in identifying reference priors. La normalité asymptotique de la loi a posterioriétant donné la valeur d'une statistiqueRésumé : Les auteursétablissent la normalité asymptotique et déterminent la variance limite de la densité a posteriori d'un paramètre multivarié,étant donné la valeur d'une statistique convergente et asymptotiquement gaussienne répondantà un théorème central limite local uniforme. Leur démonstration vaut pour le cas continu mais peutêtreétendue aux variables aléatoiresà valeurs sur un treillis. Elle s'appuie sur une expansion de Edgeworth uniforme permettant de contrôler le comportement de la statistique par laquelle on conditionne. Ils présentent des exemples et montrent en quoi leur résultat permet d'identifier des lois référentielles a priori.

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Consistency of Maximum Likelihood and Bayes Estimates

Cited by 36 publications

References 4 publications

Necessary and sufficient conditions for consistency of generalizedM-estimates

Necessary and sufficient conditions for consistency of generalizedM-estimates

Asymptotically Informative Prior for Bayesian Analysis

Asymptotic normality of the posterior given a statistic

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