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Marginal Likelihood Score-Based Tests of Regression Disturbances in the Presence of Nuisance Parameters

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  • Rahman, Shahidur
  • King, Maxwell L.

Abstract

This paper is concerned with tests of the covariance matrix of the disturbances in the linear regression model that involve nuisance parameters which cannot be eliminated by usual invariance arguments. Score-based tests, namely Lagrange multiplier (LM) and locally most mean powerful (LMMP) tests are derived from the marginal likelihood. Applications considered include (i) testing for random regression coefficients; (ii) testing for secondorder autoregressive (AR(2)) disturbances in the presence of AR(1) disturbances; and (iii) testing for ARMA(1,1) disturbances; each in the presence of AR(1) disturbances. An empirical size and power comparison shows that typically the new tests have more accurate asymPtotic critical values and slightly more power than their respective conventional counterparts.

Suggested Citation

  • Rahman, Shahidur & King, Maxwell L., "undated". "Marginal Likelihood Score-Based Tests of Regression Disturbances in the Presence of Nuisance Parameters," Department of Econometrics and Business Statistics Working Papers 267421, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:ags:monebs:267421
    DOI: 10.22004/ag.econ.267421
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    2. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    3. Jae Kim & Mahbuba Yeasmin, 2005. "The Size and Power of the Bias-Corrected Bootstrap Test for Regression Models with Autocorrelated Errors," Computational Economics, Springer;Society for Computational Economics, vol. 25(3), pages 255-267, June.
    4. Federico Martellosio, 2020. "Non-Identifiability in Network Autoregressions," Papers 2011.11084, arXiv.org, revised Jun 2022.
    5. Badi Baltagi & Seuck Heun Song & Byoung Cheol Jung, 2002. "Simple Lm Tests For The Unbalanced Nested Error Component Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 167-187.
    6. Jahar Bhowmik & Maxwell King, 2007. "Maximal invariant likelihood based testing of semi-linear models," Statistical Papers, Springer, vol. 48(3), pages 357-383, September.
    7. Marc K. Francke & Siem Jan Koopman & Aart F. De Vos, 2010. "Likelihood functions for state space models with diffuse initial conditions," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 407-414, November.
    8. Willa W. Chen & Rohit S. Deo, 2009. "The restricted likelihood ratio test at the boundary in autoregressive series," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 618-630, November.
    9. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.
    10. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
    11. Jahar L. Bhowmik & Maxwell L. King, 2005. "Parameter Estimation in Semi-Linear Models Using a Maximal Invariant Likelihood Function," Monash Econometrics and Business Statistics Working Papers 18/05, Monash University, Department of Econometrics and Business Statistics.
    12. Sriananthakumar, Sivagowry, 2013. "Testing linear regression model with AR(1) errors against a first-order dynamic linear regression model with white noise errors: A point optimal testing approach," Economic Modelling, Elsevier, vol. 33(C), pages 126-136.
    13. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.

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