On the convergence of kernel estimators of probability density functions

  • Albert E. Rust
  • Chris P. Tsokos


The properties of the characteristic function of the fixed-bandwidth kernel estimator of a probability density function are used to derive estimates of the rate of almost sure convergence of such estimators in a family of Hilbert spaces. The convergence of these estimators in a reproducing-kernel Hilbert space is used to prove the uniform convergence of variable-bandwidth estimators. An algorithm employing the fast Fourier transform and heuristic estimates of the optimal bandwidth is presented, and numerical experiments using four density functions are described.


Hilbert Space Probability Density Function True Density Kernel Estimator Optimal Bandwidth 


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1981

Authors and Affiliations

  • Albert E. Rust
    • 1
  • Chris P. Tsokos
    • 1
  1. 1.Florida Mental Health InstituteUniversity of South FloridaUSA

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