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In Fisher's net : exact F-tests in semi-parametric models with exchangeable errors

Author

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  • Frédéric Jouneau-Sion

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Olivier Torrès

    (EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé)

Abstract

We consider testing about the slope parameter β when Y - X β is assumed to be an exchangeable process conditionally on X. This framework encompasses the semi-parametric linear regression model. We show that the usual Fisher's procedure have non trivial exact rejection bound under the null hypothesis R β = ϒ. This bound derives from the Markov inequality and a close inspection of multivariate moments of self-normalized, self-centered, exchangeable processes. Improvement by higher order versions of the Markov inequality are also presented. The bounds do not require the existence of any moment, so they remain valid even if TCL do not apply. We generalize the framework to multivariate and order-1 auto-regressive models with exogenous variables.

Suggested Citation

  • Frédéric Jouneau-Sion & Olivier Torrès, 2014. "In Fisher's net : exact F-tests in semi-parametric models with exchangeable errors," Working Papers halshs-01062623, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01062623
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01062623
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    References listed on IDEAS

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    Keywords

    Exact testing; linear model; AR(1) model; multivariate model; exchangeable process;
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