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This book presents new and original research in Statistical Information Theory, based on minimum divergence estimators and test statistics, from a theoretical and applied point of view, for different statistical problems with special emphasis on efficiency and robustness. Divergence statistics, based on maximum likelihood estimators, as well as Wald’s statistics, likelihood ratio statistics and Rao’s score statistics, share several optimum asymptotic properties, but are highly non-robust in cases of model misspecification under the presence of outlying observations. It is well-known that a small deviation from the underlying assumptions on the model can have drastic effect on the performance of these classical tests. Specifically, this book presents a robust version of the classical Wald statistical test, for testing simple and composite null hypotheses for general parametric models, based on minimum divergence estimators.

n/a --- mixture index of fit --- Kullback-Leibler distance --- relative error estimation --- minimum divergence inference --- Neyman Pearson test --- influence function --- consistency --- thematic quality assessment --- asymptotic normality --- Hellinger distance --- nonparametric test --- Berstein von Mises theorem --- maximum composite likelihood estimator --- 2-alternating capacities --- efficiency --- corrupted data --- statistical distance --- robustness --- log-linear models --- representation formula --- goodness-of-fit --- general linear model --- Wald-type test statistics --- Hölder divergence --- divergence --- logarithmic super divergence --- information geometry --- sparse --- robust estimation --- relative entropy --- minimum disparity methods --- MM algorithm --- local-polynomial regression --- association models --- total variation --- Bayesian nonparametric --- ordinal classification variables --- Wald test statistic --- Wald-type test --- composite hypotheses --- compressed data --- hypothesis testing --- Bayesian semi-parametric --- single index model --- indoor localization --- composite minimum density power divergence estimator --- quasi-likelihood --- Chernoff Stein lemma --- composite likelihood --- asymptotic property --- Bregman divergence --- robust testing --- misspecified hypothesis and alternative --- least-favorable hypotheses --- location-scale family --- correlation models --- minimum penalized ?-divergence estimator --- non-quadratic distance --- robust --- semiparametric model --- divergence based testing --- measurement errors --- bootstrap distribution estimator --- generalized renyi entropy --- minimum divergence methods --- generalized linear model --- ?-divergence --- Bregman information --- iterated limits --- centroid --- model assessment --- divergence measure --- model check --- two-sample test --- Wald statistic --- Hölder divergence