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Pace, Luigi and Salvan, Alessandra and Ventura, Laura (2005) Likelihood theory, prediction, model selection: asymptotic connections. [Working Paper] WORKING PAPER SERIES, 17/2005 . , PADOVA (Inedito)

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Abstract (english)

Plug-in estimation and corresponding refinements involving penalisation have been considered in various areas of parametric statistical inference. One major example is adjustment of the profile likelihood for inference in the presence of nuisance parameters. Another important setting is prediction, where improved estimative predictive densities have been recently developed. A third related setting is model selection, where information criteria based on penalisation of maximised likelihood have been proposed starting from the pioneering contribution of Akaike. The seminal contributions in the last setting predate those introducing the former two classes of procedures, and pertinent portions of literature seem to have evolved quite independently. The aim of this paper is to establish some simple asymptotic connections among these classes of procedures. In particular, all the three kinds of penalisations involved can be viewed as bias corrections of plug-in estimates of theoretical target criteria which are shown to be very closely connected. As a by-product, we obtain adjusted profile likelihoods from optimal predictive densities. Links between adjusted procedures in likelihood theory and model selection procedures are also briefly enquired throuh some simulation studies.


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EPrint type:Working Paper
Anno di Pubblicazione:December 2005
Key Words:Akaike’s information criterion, Likelihood asymptotics, Model selection, Nuisance parameter, Predictive density, Profile likelihood.
Settori scientifico-disciplinari MIUR:Area 13 - Scienze economiche e statistiche > SECS-S/01 Statistica
Struttura di riferimento:Dipartimenti > Dipartimento di Scienze Statistiche
Codice ID:7082
Depositato il:09 Sep 2014 13:57
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