Density estimation by the penalized combinatorial method
Journal of Multivariate Analysis
About the asymptotic accuracy of Barron density estimates
IEEE Transactions on Information Theory
A note on robust hypothesis testing
IEEE Transactions on Information Theory
On Divergences and Informations in Statistics and Information Theory
IEEE Transactions on Information Theory
Robust tests based on dual divergence estimators and saddlepoint approximations
Journal of Multivariate Analysis
Dual divergence estimators and tests: Robustness results
Journal of Multivariate Analysis
Estimating divergence functionals and the likelihood ratio by convex risk minimization
IEEE Transactions on Information Theory
Information, Divergence and Risk for Binary Experiments
The Journal of Machine Learning Research
Optimal robust M-estimators using Rényi pseudodistances
Journal of Multivariate Analysis
Minimum $$K_{\phi }$$K-divergence estimators for multinomial models and applications
Computational Statistics
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We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple and composite hypotheses, extending the maximum likelihood technique. Another view of the maximum likelihood approach, for estimation and tests, is given. We prove existence and consistency of the proposed estimates. The limit laws of the estimates and test statistics (including the generalized likelihood ratio one) are given under both the null and the alternative hypotheses, and approximations of the power functions are deduced. A new procedure of construction of confidence regions, when the parameter may be a boundary value of the parameter space, is proposed. Also, a solution to the irregularity problem of the generalized likelihood ratio test pertaining to the number of components in a mixture is given, and a new test is proposed, based on @g^2-divergence on signed finite measures and the duality technique.