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1 results

  • 6 - Empirical Christoffel–Darboux Analysis

  • from Part Two - Statistics and Applications to Data Analysis
  • Jean Bernard Lasserre, Edouard Pauwels, Institut de Recherche en Informatique, Toulouse, Mihai Putinar, University of California, Santa Barbara
  • Book:
    The Christoffel–Darboux Kernel for Data Analysis
    Published online:
    31 March 2022
    Print publication:
    07 April 2022, pp 77-86

  • Summary

    For empirical measures supported on a random sample, statistical bounds describe the large-sample asymptotic behavior of the empirical Christoffel function. The Christoffel function associated with a fixed degree will converge to its population counterpart in the large-sample limit. The convergence can be made quantitative using random matrix concentration. Furthermore, in the context of singularly supported population measure, the rank will stabilize almost surely for a finite number of samples.