A General Method of Testing for Random Parameter Variation in Statistical Models

  • B. P. M. McCabe
  • S. J. Leybourne
Part of the Advanced Studies in Theoretical and Applied Econometrics book series (ASTA, volume 36)


Testing the adequacy of an estimated statistical model is a perennial problem for data analysts. If some specific alternative construction of the model is entertained—for example, if allowance should be made for autocorrelation—then it is fairly straightforward to write down specific test statistics tailored for that situation. On the other hand, in many circumstances what is required is some indication of the overall suitability of the model rather looking in some specific direction. In cases where the model can be formulated in such a way that maximum likelihood (or pseudo maximum likelihood) methods may be used, an elegant technique was introduced by White (1982) which exploits the well known information-matrix equality that holds for properly specified models. If the specified model is not consistent with the data, this equality will not hold; and this fact may be used as the basis for a general specification test.


Multivariate Statistical Analysis Random Coefficient Nonlinear Regression Model General Specification Test Pseudo Maximum Likelihood 
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  1. [1]
    Cox, D.R., (1983), Some Remarks on Overdispersion, Biometrika, 70, 269–274.CrossRefGoogle Scholar
  2. [2]
    Chesher, A.D., (1984), Testing for Neglected Heterogeneity, Econometrica, 52, 865–872.CrossRefGoogle Scholar
  3. [3]
    Fahrmeir, L., and G. Tutz, (1994), Multivariate Statistical Modelling Based on Generalised Linear Models, Springer Verlag, New York.Google Scholar
  4. [4]
    King, M.L., and P.X. Wu, (1990), Locally Optimal One-Sided Tests for Multiparameter Hypotheses, Paper Presented at the Sixth World Congress of the Econometric Society, Barcelona.Google Scholar
  5. [5]
    Kwaitowski, D., P.C.B Phillips, P. Schmidt and Y. Shin, (1992), Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure are we that Economic Time Series have a Unit Root? Journal of Econometrics, 54, 159–178.CrossRefGoogle Scholar
  6. [6]
    Leybourne, S.J., and B.P.M. McCabe, (1994), A Consistent Test for a Unit Root, Journal of Business and Economic Statistics, 12, 157–166.Google Scholar
  7. [7]
    Leybourne, S.J., B.P.M. McCabe and A.R. Tremayne, (1996), Can Economic Time Series be Differenced to Stationarity? Journal of Business and Economic Statistics, 14, 435–446.Google Scholar
  8. [8]
    Magnus, J.R., and H. Neudecker, (1988), Matrix Differential Calculus with Applications in Statistics and Econometrics, John Wiley and Sons, New York.Google Scholar
  9. [9]
    McCabe, B.P.M., and A.R. Tremayne, (1995), Testing if a Time Series is Difference Stationary, Annals of Statistics, 23, 1015–1028.CrossRefGoogle Scholar
  10. [10]
    McCullagh, P., and J.A. Neider, (1989), Generalised Linear Models, 2nd Edition, Chapman and Hall, London.Google Scholar
  11. [11]
    McCabe, B.P.M., and S.J. Leybourne, (1993), Testing for Parameter Variation in Nonlinear Regression Models, Journal of the Royal Statistical Society, Series B, 55, 133–144.Google Scholar
  12. [12]
    White, H., (1982), Maximum Likelihood Estimation of Misspecified Models, Econometrica, 50, 1–26.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • B. P. M. McCabe
  • S. J. Leybourne

There are no affiliations available

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