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Title: Robustness and confidence distributions Authors:  Laura Ventura - University of Padova (Italy) [presenting]
Erlis Ruli - University of Padova (Italy)
Monica Musio - University of Cagliari (Italy)
Abstract: Inferential topics for a parameter of interest (such as reaching point estimates, assessing their precision, setting up tests along with measures of evidence, finding confidence intervals, comparing the value of the parameter of interest with other parameters from other studies, etc.) may be automatically performed if a frequentist distribution, without prior, is available. An approach to derive a frequentist distribution is based on confidence distributions (CDs) and confidence curves. A CD analysis is much more informative than providing a confidence interval or a p-value. The standard theory for parametric inference evolves around the use of likelihood methods, and this is also partly the case for CDs. Typically, to first-order, CDs may be based on the large sample theory for the maximum likelihood estimator, the Wald statistic and the likelihood-ratio test. The basic concepts and recipes for CDs are however not limited to likelihood methods, and various alternatives may be worked with. For instance, it is well known that in the presence of model misspecifications, likelihood methods may be inaccurate. The aim is to discuss the use of robust unbiased estimating equations in order to compute a robust CD. In particular, we suggest both asymptotic robust CDs obtained by using first-order results for estimating equation inference and a simulation-based approach to CD, based on a frequentist reinterpretation of Approximate Bayesian Computation techniques.