In Fisher's Net: Exact F-Tests in Semi-Parametric Models with Exchangeable Errors

30 Pages Posted: 18 Sep 2014

See all articles by Frédéric Jouneau-Sion

Frédéric Jouneau-Sion

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE)

Torrès Olivier

University of Lille III - EQUIPPE-GREMARS

Date Written: September 10, 2014

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.

Keywords: Exact testing, linear model, AR(1) model, multivariate model, exchangeable process

JEL Classification: C01, C12, C14

Suggested Citation

Jouneau-Sion, Frédéric and Olivier, Torrès, In Fisher's Net: Exact F-Tests in Semi-Parametric Models with Exchangeable Errors (September 10, 2014). Available at SSRN: https://ssrn.com/abstract=2494209 or http://dx.doi.org/10.2139/ssrn.2494209

Frédéric Jouneau-Sion (Contact Author)

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE) ( email )

93, chemin des Mouilles
Ecully, 69130
France

Torrès Olivier

University of Lille III - EQUIPPE-GREMARS ( email )

Lille
France

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