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Optimal Pseudo-Gaussian and Rank-Based Random Coefficient Detection in Multiple Regression


  • Abdelhadi Akharif
  • Mohamed Fihri
  • Marc Hallin
  • Amal Mellouk


Random coefficient regression (RCR) models are the regression versions of random effects models in analysis of variance and panel data analysis. Optimal detection of the presence of random coefficients (equivalently, optimal testing of the hypothesis of constant regression coefficients) has been an open problem for many years. The simple regression case has been solved recently (Fihri et al. (2017)), and the multiple regression case is considered here. This problem poses several theoretical challenges (a)a nonstandard ULAN structure, with log-likelihood gradients vanishing at the null hypothesis; (b) a cone-shaped alternative under which traditional maximin-type optimality concepts are no longer adequate; (c) a matrix of nuisance parameters (the correlation structure of the random coefficients) that are not identified under the null but have a very significant impact on local powers. Inspired by Novikov (2011), we propose a new (local and asymptotic) concept of optimality for this problem, and, for specified error densities, derive the corresponding parametrically optimal procedures.A suitable modification of the Gaussian version of the latter is shown to remain valid under arbitrary densities with finite moments of order four, hence qualifies as a pseudo-Gaussian test. The asymptotic performances of those pseudo-Gaussian tests, however, are rather poor under skewed and heavy-tailed densities. We therefore also construct rank-based tests, possibly based on data-driven scores, the asymptotic relative efficiencies of which are remarkably high with respect to their pseudo-Gaussian counterparts.

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  • Abdelhadi Akharif & Mohamed Fihri & Marc Hallin & Amal Mellouk, 2018. "Optimal Pseudo-Gaussian and Rank-Based Random Coefficient Detection in Multiple Regression," Working Papers ECARES 2018-39, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/279634

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    References listed on IDEAS

    1. Marc Hallin & Abdelhadi Akharif, 2003. "Efficient detection of random coefficients in AR(p) models," ULB Institutional Repository 2013/2121, ULB -- Universite Libre de Bruxelles.
    2. Bennala, Nezar & Hallin, Marc & Paindaveine, Davy, 2012. "Pseudo-Gaussian and rank-based optimal tests for random individual effects in large n small T panels," Journal of Econometrics, Elsevier, vol. 170(1), pages 50-67.
    3. Abdelhadi Akharif & Marc Hallin, 2003. "Efficient detection of random coefficients in autoregressive models," ULB Institutional Repository 2013/127956, ULB -- Universite Libre de Bruxelles.
    4. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    5. Nezar Bennala & Marc Hallin & Davy Paindaveine, 2010. "Rank‐based Optimal Tests for Random Effects in Panel Data," Working Papers ECARES ECARES 2010-018, ULB -- Universite Libre de Bruxelles.
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    Random Coefficient; Multiple RegressionModel; Local Asymptotic Normality; Pseudo-Gaussian Test; Aligned Rank Test; Cone Alternative;

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