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The strong law of large numbers for k-means and best possible nets of Banach valued random variables
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  • Published: August 1988

The strong law of large numbers for k-means and best possible nets of Banach valued random variables

  • J. A. Cuesta1,2 &
  • C. Matran1,2 

Probability Theory and Related Fields volume 78, pages 523–534 (1988)Cite this article

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  • 44 Citations

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Summary

Let B be a uniformly convex Banach space, X a B-valued random variable and k a given positive integer number. A random sample of X is substituted by the set of k elements which minimizes a criterion. We found conditions to assure that this set converges a.s., as the sample size increases, to the set of k-elements which minimizes the same criterion for X.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Santander, Santander, Spain

    J. A. Cuesta & C. Matran

  2. Department of Statistics, University of Valladolid, Valladolid, Spain

    J. A. Cuesta & C. Matran

Authors
  1. J. A. Cuesta
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  2. C. Matran
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Cuesta, J.A., Matran, C. The strong law of large numbers for k-means and best possible nets of Banach valued random variables. Probab. Th. Rel. Fields 78, 523–534 (1988). https://doi.org/10.1007/BF00353875

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  • Received: 13 May 1985

  • Revised: 29 December 1987

  • Issue Date: August 1988

  • DOI: https://doi.org/10.1007/BF00353875

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Keywords

  • Banach Space
  • Positive Integer
  • Assure
  • Random Sample
  • Stochastic Process
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