Broniatowski, Michel; Keziou, Amor Parametric estimation and tests through divergences and the duality technique. (English) Zbl 1151.62023 J. Multivariate Anal. 100, No. 1, 16-36 (2009). Summary: We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. The 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 \(\chi ^{2}\)-divergence on signed finite measures and the duality technique. Cited in 2 ReviewsCited in 37 Documents MSC: 62F12 Asymptotic properties of parametric estimators 62F25 Parametric tolerance and confidence regions 62F03 Parametric hypothesis testing 62F10 Point estimation 62E20 Asymptotic distribution theory in statistics Keywords:parametric estimation; parametric test; maximum likelihood; mixture; boundary valued parameter; power function; duality; \(\phi\)-divergence; Fenchel duality × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL References: [1] Basu, A.; Lindsay, B. 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