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The Effect of Nonnormality

Published online by Cambridge University Press:  11 February 2009

Offer Lieberman
Offer Lieberman
Affiliation:
Technion–Israel Institute of Technology
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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.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 1 , February 1997 , pp. 52 - 78
Copyright
Copyright © Cambridge University Press 1997

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