Mathematical Sciences: Projective Score Methods and Approximate Conditional Inference

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A common theme to the areas of research described in this proposal is the presence of nuisance parameters and the necessity of removing an estimation bias in the parameter of interest, induced by the estimation of the nuisance parameters. The reason why the bias must be removed is that it may lead to inconsistency in the maximum likelihood estimator of the parameter of interest. The projects all use a projective approach to modify the score function for the parameter of interest, so that the bias attributable to the estimation of the nuisance parameter is reduced. The benefits of reducing bias will transfer to more accurate parameter estimates, confidence intervals with better coverage rates and test statistics that for small sample sizes have distributions "closer" to their asymptotic limiting distributions. We live in an age where information, that is data, is abundant. Our statistical understanding of this data arises from making accurate models. The large data sets that we have at hand show that simple models rarely fit the data well, and so we are led to consider more complex models with many unknowns. The proposed research will address the practical implementation and interpretative issues involved with these rich statistical models involving many variables.