IDEAS home Printed from https://ideas.repec.org/p/eca/wpaper/2013-279634.html
   My bibliography  Save this paper

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

Author

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

Abstract

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/279634/3/2018-39-AKHARIF_FIHRI_HALLIN_MELLOUCK-optimal.pdf
    File Function: Œuvre complète ou partie de l'œuvre
    Download Restriction: no

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Random Coefficient; Multiple RegressionModel; Local Asymptotic Normality; Pseudo-Gaussian Test; Aligned Rank Test; Cone Alternative;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eca:wpaper:2013/279634. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Benoit Pauwels). General contact details of provider: http://edirc.repec.org/data/arulbbe.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.