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On the estimation of monotone uniform approximations

Author

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  • Domínguez-Menchero, J. S.
  • López-Palomo, M. J.

Abstract

This paper studies the estimation of L[infinity]-best monotone approximations to a - known or unknown - function H. When H is known, natural empirical estimates are pointwise consistent and also uniform consistent under an extra continuity condition. When H is unknown, a preliminary uniform estimation of H is shown to be necessary so that the method can be applied to this estimate instead of H. However, some points of application do not allow this possibility and therefore a more general procedure of monotone approximation through appropriate sample subsets is investigated. It is shown to be pointwise consistent, and a uniform consistency through these subsets is also assured. The method is applied in Nonparametric Regression.

Suggested Citation

  • Domínguez-Menchero, J. S. & López-Palomo, M. J., 1997. "On the estimation of monotone uniform approximations," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 355-362, November.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:4:p:355-362
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