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. 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.
    4. Abdelhadi Akharif & Marc Hallin, 2003. "Efficient detection of random coefficients in autoregressive models," ULB Institutional Repository 2013/127956, ULB -- Universite Libre de Bruxelles.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dong Jin Lee, 2016. "Parametric and Semi-Parametric Efficient Tests for Parameter Instability," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 451-475, July.
    2. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    3. Marc Hallin & Ramon van den Akker & Bas Werker, 2013. "On Quadratic Expansions of Log-Likelihoods and a General Asymptotic Linearity Result," Working Papers ECARES ECARES 2013-34, ULB -- Universite Libre de Bruxelles.
    4. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    5. 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.
    6. Sukru Acitas & Pelin Kasap & Birdal Senoglu & Olcay Arslan, 2013. "One-step M -estimators: Jones and Faddy's skewed t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1545-1560, July.
    7. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2016. "Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution," International Journal of Forecasting, Elsevier, vol. 32(2), pages 437-457.
    8. Michael S. Smith & Shaun P. Vahey, 2016. "Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 416-434, July.
    9. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    10. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2012. "Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 732-740.
    11. Panagiotelis, Anastasios & Smith, Michael, 2010. "Bayesian skew selection for multivariate models," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1824-1839, July.
    12. André Lucas & Bernd Schwaab & Xin Zhang, 2017. "Modeling Financial Sector Joint Tail Risk in the Euro Area," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 171-191, January.
    13. Baumeister, Christiane & Hamilton, James D., 2018. "Inference in structural vector autoregressions when the identifying assumptions are not fully believed: Re-evaluating the role of monetary policy in economic fluctuations," Journal of Monetary Economics, Elsevier, vol. 100(C), pages 48-65.
    14. González-Rivera, Gloria & Maldonado, Javier & Ruiz, Esther, 2019. "Growth in stress," International Journal of Forecasting, Elsevier, vol. 35(3), pages 948-966.
    15. Kahrari, F. & Rezaei, M. & Yousefzadeh, F. & Arellano-Valle, R.B., 2016. "On the multivariate skew-normal-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 80-88.
    16. Xu, Wenjing & Pan, Qing & Gastwirth, Joseph L., 2014. "Cox proportional hazards models with frailty for negatively correlated employment processes," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 295-307.
    17. Mitchell, James & Weale, Martin, 2019. "Forecasting with Unknown Unknowns: Censoring and Fat Tails on the Bank of England's Monetary Policy Committee," EMF Research Papers 27, Economic Modelling and Forecasting Group.
    18. S. Cabras & M. E. Castellanos, 2009. "Default Bayesian goodness-of-fit tests for the skew-normal model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 223-232.
    19. Tobias Adrian & Nina Boyarchenko & Domenico Giannone, 2019. "Vulnerable Growth," American Economic Review, American Economic Association, vol. 109(4), pages 1263-1289, April.
    20. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.

    More about this item

    Keywords

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

    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: . General contact details of provider: https://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 bibliographic 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.

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

    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.