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Lun. 23/10/2017 11:00 K71, Bâtiment K, RdC

JOUNEAU-SION Frédéric (Université Lumière Lyon 2)
In Fisher’s net : exact F-tests in semi-parametric models with exchangeable errors


We consider testing about the parameter β when Y − Xβ is assumed to be
an exchangeable process conditionally on X. This framework encompasses the
semi-parametric linear regression model. It is shown that the usual Fisher’s pro-
cedure have non trivial exact rejection bound under the null hypothesis Rβ = γ.
This bound derives from the Markov inequality and a close inspection of multi-
variate moments of self-normalized, self-centered, exchangeable processes. Im-
provement by higher order versions of the Markov inequality are also presented.
As no existence of moments is required, the bound remains valid even if Central
Limit Theorem fails.
Three generalizations of the framework are discussed. First, the case of
possibly non-linear regression models with endogenous explanatory variables is
considered. Second, a test procedure for order–1 auto–regressive models with
exogenous variables is proposed. Third, extensions to the multivariate case
(more precisely the Wilk’s ratio test) are examined.

Pour plus d'informations, merci de contacter Cugliari J.