Abstract
The kurtosis of a random variable is often measured by its fourth standardized moment. Similarly, measures of multivariate kurtosis are often functions of a matrix containing all the fourth order moments which can be obtained from a standardized random vector. This paper examines some properties of the fourth moment matrix, and uses them to establish some inequalities between well-known scalar measures of multivariate kurtosis. Theoretical results are applied to multivariate financial returns.
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