Uniform estimation of isobars

Marie-Françoise Barme-Delcroix and Margarida Brito

Statistics & Probability Letters, 2019, vol. 148, issue C, 94-100

Abstract: The ordering of a multivariate sample is not natural and several definitions have been proposed in the literature. We consider here a multivariate sample ordered according to an increasing family of conditional quantile surfaces, isobar surfaces. We introduce a nonparametric estimator, called isogram, and establish the uniform a.s. consistency of these estimators. In particular, we show that, under some regularity conditions, the strong behaviour of the isograms is determined by the corresponding behaviour of suitable defined histogram-type estimators of the underlying conditional distribution function. Consequently, we begin our study by investigating the strong limiting behaviour of these estimators.

Keywords: Empirical functions; Nonparametric estimation; Multivariate samples; Order statistics; Uniform a.s. consistency (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.01.012

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