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A limit theorem for average dimensions

Author

Listed:
  • Shukhman Boris V.

    (1H-580 Place de la Fontaine, Montreal, QC, Canada)

  • Sobol Ilya M.

    (Keldysh Institute of Applied Mathematics, 4, Miusskaya sq., Moscow, 125047, Russia)

Abstract

A family of d-dimensional functions is introduced. It includes the test functions that in [Monte Carlo Methods Appl. 20 (2014), no. 3, 167–171] demonstrate the efficiency of certain quasi-Monte Carlo integrations. The average dimensions of these d-dimensional functions converge as d → ∞.

Suggested Citation

  • Shukhman Boris V. & Sobol Ilya M., 2015. "A limit theorem for average dimensions," Monte Carlo Methods and Applications, De Gruyter, vol. 21(2), pages 175-178, June.
    • Handle: RePEc:bpj:mcmeap:v:21:y:2015:i:2:p:175-178:n:6
    DOI: 10.1515/mcma-2014-0018
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    References listed on IDEAS

    as
    1. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
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