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Statistics in Transition New Series
Polish Statistical Association
Central Statistical Office of Poland
Subject: Economics, Statistics & Probability
ISSN: 1234-7655
eISSN: 2450-0291
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ESTIMATION OF THE CENTRAL MOMENTS OF A RANDOM VECTOR BASED ON THE DEFINITION OF THE POWER OF A VECTOR
Keywords : central moment of a random vector, estimator, multivariate distribution, power of a vector.
Citation Information : Statistics in Transition New Series. Volume 18, Issue 1, Pages 1-20, DOI: https://doi.org/10.21307/stattrans-2016-061
License : (CC BY 4.0)
Published Online: 03-July-2017
- ARTICLE
- FIGURES & TABLES
- REFERENCES
- EXTRA FILES
- COMMENTS
ARTICLE
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.
FIGURES & TABLES
REFERENCES
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