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Title: Higher-order robust inference Authors:  Elvezio Ronchetti - University of Geneva (Switzerland) [presenting]
Abstract: Robust statistics develops statistical procedures which are still reliable in the presence of small deviations from the assumed model. Their statistical properties are typically based on approximations obtained by first-order asymptotic theory. However, when the sample size is moderate to small or even in large samples when probabilities in the tails are required, first-order asymptotic analysis is often too inaccurate. We review a class of techniques which combine robustness and higher-order accuracy. They are derived using saddlepoint methods and provide robust tests for testing hypotheses on the parameters and for overidentification which are second-order correct in terms of relative error. Their nonparametric versions are linked to empirical likelihood methods and exhibit good accuracy in finite samples even in the presence of model misspecifications. The theory is illustrated in several important domains, including generalized linear models, quantile regression, composite likelihood, measurement error models, indirect inference, and time series in the frequency domain.