On the estimation of monotone uniform approximations

J. S. Domínguez-Menchero and M. J. López-Palomo

Statistics & Probability Letters, 1997, vol. 35, issue 4, 355-362

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.

Keywords: L[infinity]-best; monotone; approximations; L[infinity]-Dip; Uniform; consistency; Regression; function; Kernel; regression; estimate (search for similar items in EconPapers)
Date: 1997
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