Parametric estimation and tests through divergences and the duality technique

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Broniatowski, Michel²  Keziou, Amor^1,2 

[1] Univ Reims, Math Lab, UMR 6056, F-51100 Reims, France

[2] Univ Paris 06, LSTA, F-75252 Paris 05, France

关键词: Parametric estimation;    Parametric test;    Maximum likelihood;    Mixture;    Boundary valued parameter;    Power function;    Duality;    phi-divergence;   

DOI  :  10.1016/j.jmva.2008.03.011

来源: Elsevier

【 摘 要 】

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 chi(2)-divergence on signed finite measures and the duality technique. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free