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Polygonal smoothing of the empirical distribution function

Author

Listed:
  • D. Blanke

    (Avignon University, LMA EA2151)

  • D. Bosq

    (Sorbonne Université, CNRS, Laboratoire de Probabilités, Statistique et Modélisation, LPSM)

Abstract

We present two families of polygonal estimators of the distribution function: the first family is based on the knowledge of the support while the second addresses the case of an unknown support. Polygonal smoothing is a simple and natural method for regularizing the empirical distribution function $$F_n$$ F n but its properties have not been studied deeply. First, consistency and exponential type inequalities are derived from well-known convergence properties of $$F_n$$ F n . Then, we study their mean integrated squared error (MISE) and we establish that polygonal estimators may improve the MISE of $$F_n$$ F n . We conclude by some numerical results to compare these estimators globally, and also together with the integrated kernel distribution estimator.

Suggested Citation

  • D. Blanke & D. Bosq, 2018. "Polygonal smoothing of the empirical distribution function," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 263-287, July.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:2:d:10.1007_s11203-018-9183-y
    DOI: 10.1007/s11203-018-9183-y
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    References listed on IDEAS

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