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A note on the representation of \({E\left({\textit{\textbf {x}}}\otimes {\textit{\textbf {xx}}}^{\prime}\right) }\) and \({E\left({\textit{\textbf {xx}}}^{\prime }\otimes {\textit{\textbf {xx}}}^{\prime }\right)}\) for the random vector x

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Abstract

In this paper we consider \({E(x\otimes xx^{\prime})}\) and \({E(xx^{\prime }\otimes xx^{\prime})}\) for a random vector x where x i has existing moments up to the fourth order and where the higher moments may depend on i. This extends previous results which assumed a common higher moment and E(xx′) = I.

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Authors and Affiliations

  1. Department of Statistics, Uppsala University, P.O. Box 513, 751 20, Uppsala, Sweden

    Johan Lyhagen

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  1. Johan Lyhagen
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Correspondence to Johan Lyhagen.

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Lyhagen, J. A note on the representation of \({E\left({\textit{\textbf {x}}}\otimes {\textit{\textbf {xx}}}^{\prime}\right) }\) and \({E\left({\textit{\textbf {xx}}}^{\prime }\otimes {\textit{\textbf {xx}}}^{\prime }\right)}\) for the random vector x . Stat Papers 53, 697–701 (2012). https://doi.org/10.1007/s00362-011-0373-6

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  • DOI: https://doi.org/10.1007/s00362-011-0373-6

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