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Uniform convergence rates for nonparametric estimators smoothed by the beta kernel

Author

Listed:
  • Masayuki Hirukawa
  • Irina Murtazashvili
  • Artem Prokhorov

Abstract

This paper provides a set of uniform consistency results with rates for nonparametric density and regression estimators smoothed by the beta kernel having support on the unit interval. Weak and strong uniform convergence is explored on the basis of expanding compact sets and general sequences of smoothing parameters. The results in this paper are useful for asymptotic analysis of two‐step semiparametric estimation using a first‐step kernel estimate as a plug‐in. We provide simulations and a real data example illustrating attractive properties of the estimators.

Suggested Citation

  • Masayuki Hirukawa & Irina Murtazashvili & Artem Prokhorov, 2022. "Uniform convergence rates for nonparametric estimators smoothed by the beta kernel," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1353-1382, September.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:3:p:1353-1382
    DOI: 10.1111/sjos.12573
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    Cited by:

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