Abstract
C. R. Rao has contributed to a broad variety of statistics, including linear models, Fisher information, multivariate analysis and matrix theory. This article extends a line of Rao’s research, which exploits properties of Fisher information to derive or rederive analytic inequalities. In this article, properties of Fisher information are applied to mixed Gaussian distributions to yield a matrix mean function which lies between the arithmetic and harmonic means, analogous to the geometric mean. Fisher information also yields a generalized weighted arithmetic–harmonic mean inequality.
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Kagan, A.M., Smith, P.J. (2021). Statistical Meaning of Mean Functions: A Novel Matrix Mean Derived from Fisher Information. In: Arnold, B.C., Balakrishnan, N., Coelho, C.A. (eds) Methodology and Applications of Statistics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-83670-2_2
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DOI: https://doi.org/10.1007/978-3-030-83670-2_2
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