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Marginal Likelihood Based Tests of a Subvector of the Parameter Vector of Linear Regression Disturbances

Author

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  • Ara, I.
  • King, M.L.

Abstract

This paper is concerned with the problem of testing a subset of the parameters which characterize the error variance-covariance matrix in the general linear regression model. Formulae for likelihood ratio, Wald, Lagrange multiplier and asymptotically locally most mean powerful test statistics based on the likelihood of a maximal invariant statistic or an equivalent marginal likelihood are given. Specific applications discussed are the problems of testing against AR(4) disturbances in the presence of AR(1) disturbances and testing for a Hildreth-Houck (1968) random coefficient against the alternative of a Rosenberg (1973) random coefficient. Monte Carlo size and power calculations for these two testing problems are reported. These results provide further evidence that supports the proposed approach to test construction. It also suggests that better handling of nuisance parameters is likely to improve the small-sample properties of asymptotically based inference procedures.
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Suggested Citation

  • Ara, I. & King, M.L., 1995. "Marginal Likelihood Based Tests of a Subvector of the Parameter Vector of Linear Regression Disturbances," Monash Econometrics and Business Statistics Working Papers 12/95, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:1995-12
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    Cited by:

    1. Rahman, Shahidur & King, Maxwell L., 1997. "Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 82(1), pages 81-106.
    2. Jahar Bhowmik & Maxwell King, 2007. "Maximal invariant likelihood based testing of semi-linear models," Statistical Papers, Springer, vol. 48(3), pages 357-383, September.
    3. Laskar, Mizan R. & King, Maxwell L., 1997. "Modified Wald test for regression disturbances," Economics Letters, Elsevier, vol. 56(1), pages 5-11, September.
    4. 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.

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