Estimation of the central moments of a random vector based on the  definition of the power of a vector

Katarzyna  Budny

doi:https://doi.org/10.59170/stattrans-2017-001

Estimation of the central moments of a random vector based on the definition of the power of a vector

Katarzyna Budny Cracow University of Economics. Statistics in Transition new series, vol. 18, 2017, 1, pages: 7-26 Published online: 1 March 2017 https://doi.org/10.59170/stattrans-2017-001

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ABSTRACT

The moments of a random vector based on the definition of the power of a vector, proposed by J. Tatar, are scalar and vector characteristics of a multivariate distribution. Analogously to the univariate case, we distinguish the uncorrected and the central moments of a random vector. Other characteristics of a multivariate distribution, i.e. an index of skewness and kurtosis, have been introduced by using the central moments of a random vector. For the application of the mentioned quantities for the analysis of multivariate empirical data, it appears desirable to construct their respective estimators. This paper presents the consistent estimators of the central moments of a random vector, for which essential characteristics have been found, such as a mean vector and a mean squared error. In these formulas, the relevant orders of approximation have been taken into account.

KEYWORDS

central moment of a random vector, estimator, multivariate distribution, power of a vector.

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