ESTIMATION OF THE CENTRAL MOMENTS OF A RANDOM VECTOR BASED ON THE DEFINITION OF THE POWER OF A VECTOR

Katarzyna Budny
2017 Statistics in Transition New Series  
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
more » ... oned 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.
doi:10.21307/stattrans-2016-061 fatcat:bglxh2two5g7ln36utpwtshp3i