Di Caterina, Claudia (2017) Reducing the Impact of Bias in Likelihood Inference for Prominent Model Settings. [Ph.D. thesis]
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The existence of bias in inferential procedures based on the likelihood function has given rise to a great deal of research in the statistical literature. The magnitude of such bias plays a crucial role in estimation: if large, misleading conclusions on the quantities of interest are likely to be drawn. This is a matter of serious concern when the available sample size is small to moderate or when the model under study does not meet the regularity conditions for usually reliable maximum likelihood inference. In the present thesis, we attempt to reduce the impact of bias in both these circumstances, by following distinct paths. For finite-sample problems, we propose a convenient way to refine Wald-type inference in regression settings through asymptotic bias correction of the -statistic. Such approach stems from the intuition of seeing that pivot as the estimator of a model reparametrization. For non-regular problems, with special focus on scenarios characterized by the presence of incidental parameters, we suggest a strategy to extend the current range of applications of the modified profile likelihood. This solution, founded on Monte Carlo simulation, is versatile enough to cope with several nonstandard modeling frameworks for grouped data.
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