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The Effect of Nonnormality

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  • Lieberman, Offer

Abstract

A typical statistic encountered can be characterized as a ratio of polynomials of arbitrary degree in a random vector. This vector may possess any admissible cumulant structure. We provide in this paper general formulae for the effect of nonnormality on the density and distribution functions of this ratio. The results appear in terms of generalized cumulants, a theory developed by McCullagh (1984, Biometrika 71, 461–476). With the aid of suitable notation, the expressions are applied to the distributions of tests for heteroskedasticity and autocorrelation, the least-squares estimator of the autoregressive coefficient in a dynamic model, and tests for linear restrictions.

Suggested Citation

  • Lieberman, Offer, 1997. "The Effect of Nonnormality," Econometric Theory, Cambridge University Press, vol. 13(1), pages 52-78, February.
    • Handle: RePEc:cup:etheor:v:13:y:1997:i:01:p:52-78_00
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    Cited by:

    1. Qian Chen & David E. Giles, 2007. "A Saddlepoint Approximation to the Distribution of the Half-Life Estimator in an Autoregressive Model: New Insights Into the PPP Puzzle," Econometrics Working Papers 0703, Department of Economics, University of Victoria.
    2. 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.
    3. Pilar Rivera & Albert Satorra, 2000. "Country effects in ISSP-1993 environmental data: Comparison of SEM approaches," Economics Working Papers 458, Department of Economics and Business, Universitat Pompeu Fabra.

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