Évènements

In this talk, we present some inference methods in some multivariate models with
multiple unknown change-points when the target parameter is suspected to satisfy an uncertain constraint. We waive the assumptions on the error terms and establish the joint asymptotic normality of the unrestricted estimator and the restricted estimator. Further, we propose a class of shrinkage estimators that includes as a special case the unrestricted estimator, the estimator restricted as well as James-Stein type estimators. To study the performance of the proposed estimators, we generalize some classical identities underlying the multivariate Gaussian random samples or, more generally, the multivariate elliptically contoured random samples. Finally, we prove that shrinkage estimators dominate the unrestricted estimator.

Categorified principal bundles are bundles whose fibres are Lie groupoids, on which a monoidal Lie groupoid (« Lie 2-group ») acts. They are global, geometric representatives of Giraud’s non-abelian cohomology. I will talk about connections on categorified principal bundles; these realize the Breen-Messing differential refinement of non-abelian cohomology. I will explain a mechanism of parallel transport, which goes very nicely with the fibrewise Lie groupoid structure. For example, the parallel transport along a path is a Morita equivalence between the fibres over its end points.

Clifford qaudratic forms (abbreviated by CQF) were introduced in [T. Kogiso and F. Sato, J. Math. Sci. , Univ. Tokyo, 23 (2016), 791–866] as examples of non-prehomogeous type plynomials which satisfy local functional equations. In this talk, I introduce the following applications and properties of CQFs. CQFs are counter examples of Etingof , Kahzdan and Polishachuk’s problem (2002) of homaloidal polynomials. LFE of polarization of CQF keeps non-prehomogeneity. Certain phenomena suggesting the relationship between CQF and some class of Clifford Klein forms introduced by Kobayashi and Yoshino.