English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Estimators derived from a divergence criterion such as $\varphi-$divergencesare generally more robust than the maximum likelihood ones. We are interestedin particular in the so-called MD$\varphi$DE, an estimator built using a dualrepresentation of $\varphi$--divergences. We present in this paper an iterativeproximal point algorithm which permits to calculate such estimator. Thisalgorithm contains by its construction the well-known EM algorithm. Our work isbased on the paper of \citep{Tseng} on the likelihood function. We provideseveral convergence properties of the sequence generated by the algorithm, andimprove the existing results by relaxing the identifiability condition on theproximal term, a condition which is not verified for most mixture models andhard to be verified for non mixture ones. Since convergence analysis usesregularity conditions (continuity and differentiability) of the objectivefunction, which has a supremal form, we find it useful to present someanalytical approaches for studying such functions. Convergence of the EMalgorithm is discussed here again in a Gaussian and Weibull mixtures in thespirit of our approach. Simulations are provided to confirm the validity of ourwork and the robustness of the resulting estimators against outliers.

A Proximal Point Algorithm for Minimum Divergence Estimators with Application to Mixture Models