Probability Theory and Related Fields

, Volume 78, Issue 4, pp 523–534

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

  • J. A. Cuesta
  • C. Matran
Article

DOI: 10.1007/BF00353875

Cite this article as:
Cuesta, J.A. & Matran, C. Probab. Th. Rel. Fields (1988) 78: 523. doi:10.1007/BF00353875

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.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. A. Cuesta
    • 1
    • 2
  • C. Matran
    • 1
    • 2
  1. 1.Department of StatisticsUniversity of SantanderSantanderSpain
  2. 2.Department of StatisticsUniversity of ValladolidValladolidSpain