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Uniform estimation of isobars

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  • Barme-Delcroix, Marie-Françoise
  • Brito, Margarida

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.

Suggested Citation

  • Barme-Delcroix, Marie-Françoise & Brito, Margarida, 2019. "Uniform estimation of isobars," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 94-100.
    • Handle: RePEc:eee:stapro:v:148:y:2019:i:c:p:94-100
    DOI: 10.1016/j.spl.2019.01.012
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    References listed on IDEAS

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    1. Mukhopadhyay, Nitai D. & Chatterjee, Snigdhansu, 2011. "High dimensional data analysis using multivariate generalized spatial quantiles," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 768-780, April.
    2. Robert Serfling, 2002. "Quantile functions for multivariate analysis: approaches and applications," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 214-232, May.
    3. Jacob, P. & Suquet, Ch., 1997. "Regression and asymptotical location of a multivariate sample," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 173-179, September.
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