arXiv subjects
Publications and source records attributed to Michel Broniatowski.
This paper introduces a new Importance Sampling scheme, called Adaptive Twisted Importance Sampling, which is adequate for the improved estimation of rare event probabilities in he range of moderate deviations pertaining to the empirical mean of real i.i.d. summands. It is based on a sharp approximation of the density of long runs extracted from a random walk conditioned on its end value.
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 maximum likelihood technique. An other view at the maximum likelihood approach, for estimation and test, 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 both under the null and the alternative hypotheses, and approximation of the power functions is 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 $χ^{2}$-divergence on signed finite measures and duality technique.
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical likelihood (EL) method and share common features with generalized empirical likelihood (GEL). We treat the problems of existence and characterization of the divergence projections of probability measures on sets of signed finite measures. Our approach allows for a study of the estimates under misspecification. The asymptotic behavior of the proposed estimates are studied using the dual representation of the divergences and the explicit forms of the divergence projections. We discuss the problem of the choice of the divergence under various respects. Also we handle efficiency and robustness properties of minimum divergence estimates. A simulation study shows that the Hellinger divergence enjoys good efficiency and robustness properties.