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On the Asymptotic Efficiency of Directional Models Checks for Regression

In: From Statistics to Mathematical Finance

Author

Listed:
  • Miguel A. Delgado

    (Universidad Carlos III de Madrid)

  • Juan Carlos Escanciano

    (Indiana University)

Abstract

In a landmark paper, Stute (1997), Annals of Statistics) introduced smooth and directional tests for homoskedastic regression models based on weighted averages of estimated principal components of the CUSUM of residual concomitants process. This article shows that Stute’s (1997) directional test is asymptotically uniformly most powerful in a semiparametric context, considering the joint distribution of the regression error term and the covariate as a nuisance parameter. Moreover, the directional test is shown to be asymptotically equivalent to the classical t-ratio under homoskedasticity. This article also studies the heteroskedastic case, where the directional test based on the CUSUM of standarized residual concomitants (Stute et al. (1998), Annals of Statistics) is asymptotically equivalent to the semiparametric efficient test, which is the t-ratio using the generalized least squares estimator.

Suggested Citation

  • Miguel A. Delgado & Juan Carlos Escanciano, 2017. "On the Asymptotic Efficiency of Directional Models Checks for Regression," Springer Books, in: Dietmar Ferger & Wenceslao González Manteiga & Thorsten Schmidt & Jane-Ling Wang (ed.), From Statistics to Mathematical Finance, chapter 0, pages 71-87, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-50986-0_5
    DOI: 10.1007/978-3-319-50986-0_5
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