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The Extreme Linear Predictions of the Matrix-Valued Stationary Stochastic Processes

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Mathematical Statistics and Probability Theory

Summary

Let A be an arbitrary matrix with complex entries. It is known that the arithmetic mean of the diagonal elements of AA* is used for the measure of error of the linear predictions of matrix-valued stationary stochastic processes. It can be raised the question what happens if we apply another means of these diagonal elements. In this paper we use the geometric and harmonic means besides the arithmetic one for that purpose.

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References

  1. Gyires, B. ‘A generalization of a theorem of Szego’. Publ. of the Math. Inst, of the Hung. Acad, of Sciences, Vol. VIII. Ser. A. (1962). 43–51.

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  2. Gyires, B. ‘On the uncertainty of matrix-valued predictions’. Proc of the coll. on information theory. Edited by A. Rényi. János Bolyai Math. Soc. Budapest, 1968.

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  3. Helson, H. and Lowdenslager, D. ‘Prediction theory and Fourier series in several variables’. Acta Math. 99 (1958) 145–158.

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  4. Löwner, K. ‘Über monotone Matrixfunktionen’. Math. Zeitschr. 38 (1934), 177–216.

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  5. Marcus, M. ‘The permanent analogue of the Hadamard determinant theorem’. Bull. Amer. Math. Soc. 69 (1963), 494–496.

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  6. Marcus, M. ’The Hadamard theorem for permanents’. Proc. Amer. Math. Soc. 15 (1964), 967–973.

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  7. Szász,O. ‘Über die Verallgemeinerung des Hadamardschen Determinantensatzes’. Monatsh. f. Math, u. Phys. 28 (1917), 253–257.

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Author information

Authors and Affiliations

  1. Kossuth L. University, Debrecen, P.O. Box 12, 4010, Debrecen, Hungary

    B. Gyires

Authors
  1. B. Gyires
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Editor information

Editors and Affiliations

  1. University of Cologne, Germany

    P. Bauer

  2. University of Agriculture, Vienna, Austria

    F. Konecny

  3. Technical University, Vienna, Austria

    W. Wertz

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© 1987 D. Reidel Publishing Company

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Gyires, B. (1987). The Extreme Linear Predictions of the Matrix-Valued Stationary Stochastic Processes. In: Bauer, P., Konecny, F., Wertz, W. (eds) Mathematical Statistics and Probability Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3965-3_11

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  • DOI: https://doi.org/10.1007/978-94-009-3965-3_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8259-4

  • Online ISBN: 978-94-009-3965-3

  • eBook Packages: Springer Book Archive

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