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

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

Author(s): Katarzyna Budny
Subject(s): Economy, National Economy, Micro-Economics, Public Finances, Socio-Economic Research
Published by: Główny Urząd Statystyczny
Keywords: central moment of a random vector; estimator; multivariate distribution; power of a vector

Summary/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.

  • Issue Year: 18/2017
  • Issue No: 1
  • Page Range: 1-20
  • Page Count: 20
  • Language: English
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