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Some statistical properties of Hadamard products of random matrices

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Abstract

The mean of the Hadamard product of two linear combinations of a random matrix is presented in terms of the mean and variance of the random matrix for any distribution. The variance is given for the normal distribution. Further, the means of four Hadamard products of matrix bilinear forms in a normally distributed random matrix are given. Finally, the mean of a quadruple Hadamard product of linear combinations is derived under normality.

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Authors and Affiliations

  1. Department of Economics, University of Amsterdam, Roetersstraat 11, 1018, Amsterdam, WB, The Netherlands

    Heinz Neudecker

  2. School of Mathematical Sciences, Australian National University, ACT 0200, Canberra, Australia

    Shuangzhe Liu

Authors
  1. Heinz Neudecker
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  2. Shuangzhe Liu
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Correspondence to Heinz Neudecker or Shuangzhe Liu.

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Neudecker, H., Liu, S. Some statistical properties of Hadamard products of random matrices. Statistical Papers 42, 475–487 (2001). https://doi.org/10.1007/s003620100074

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  • DOI: https://doi.org/10.1007/s003620100074

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