We develop inference procedures robust to general forms of weak dependence. The use test statistics constructed by resampling data in a manner that does not depend on the unknown correlation structure data. prove are asymptotically normal under requirement target parameter can be consistently estimated at parametric rate. This holds for regular estimators many well-known dependence and justifie...

Since the seminal work of Gilboa and Schmeidler [28, p. 142] a relation between decision making under ambiguity and robust Bayesian statistics has been hinted at, and indeed immediate similarities are quite evident. At the same time, a formal treatment of this topic and a complete characterization of the relation between the two approaches is still missing. The object of this paper is to …ll th...

Sample estimates of moments and cumulants are known to be unstable in the presence of outliers. This problem is especially severe for higher order statistics, like kurtosis, which are used in algorithms for independent components analysis and projection pursuit. In this paper we propose robust generalizations of moments and cumulants that are more insensitive to outliers but at the same time re...

We present a blind multiframe image-deconvolution method based on robust statistics. The usual shortcomings of iterative optimization of the likelihood function are alleviated by minimizing theM -scale of the residuals, which achieves more uniform convergence across the image. We focus on the deconvolution of astronomical images, which are among the most challenging due to their huge dynamic ra...

An important part of the legacy of Evarist Giné is his fundamental contributions to our understanding of U -statistics and U -processes. In this paper we discuss the estimation of the mean of multivariate functions in case of possibly heavy-tailed distributions. In such situations, reliable estimates of the mean cannot be obtained by usual U -statistics. We introduce a new estimator, based on t...