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Test localmente più potenti tra gli invarianti per la verifica dell'ipotesi di normalità
No full textAdjustements of the profile likelihood from a new perspective.
Full text linkVarious modifications of the profile likelihood have been proposed over the past twenty years. Their main theoretical basis is higher-order approximation of some target likelihood, defined by a suitable model reduction via conditioning or marginalisation, where the reduced model is indexed only by the parameter of interest. However, an exact reduced target likelihood exists only for special classes of models. In this paper, a general target likelihood is defined through model restriction along the least favourable curve in the parameter space. The profile likelihood can be seen as a purely estimative counterpart of this least favourable target likelihood. We will show that various modifications of the profile likelihood arise by refining the estimation process. In particular, bias reduction of the profile loglikelihood as an estimate of the expectation of the least favourable target loglikelihood gives adjustments that coincide to second order and agree with the available adjustments
Asymptotic equivalence of conditional median unbiased and maximum likelihood estimators in exponential families
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Luigi Pace and Alessandra Salvan’s contribution to the Discussion of ‘Safe Testing’ by Peter Grünwald, Rianne de Heide and Wouter Koolen
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Tensors and likelihood expansions in the presence of nuisance parameters
No full textStochastic expansions of likelihood quantities are usually derived through ordinary Taylor expansions, rearranging terms according to their asymptotic order. The most convenient form for such expansions involves the score function, the expected information, higher order log-likelihood derivatives and their expectations. Expansions of this form are called expected/observed. If the quantity expanded is invariant or, more generally, a tensor under reparameterisations, the entire contribution of a given asymptotic order to the expected/observed expansion will follow the same transformation law. When there are no nuisance parameters, explicit representations through appropriate tensors are available. In this paper, we analyse the geometric structure of expected/observed likelihood expansions when nuisance parameters are present. We outline the derivation of likelihood quantities which behave as tensors under interest-respecting reparameterisations. This allows us to write the usual stochastic expansions of profile likelihood quantities in an explicitly tensorial form
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