Conditional cumulative distribution function for surrogate scalar response

Mounir Boumahdi (), Ali Laksaci (), Idir Ouassou () and Mustapha Rachdi ()
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Mounir Boumahdi: Hassan II University
Ali Laksaci: King Khalid University
Idir Ouassou: Cadi Ayyad University
Mustapha Rachdi: University of Grenoble Alpes

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 6, No 25, 1349-1365

Abstract: Abstract This paper aims to estimate the conditional cumulative distribution function of a surrogate scalar response given a functional random response. We construct the conditional cumulative distribution function using both the available (true) response data and the surrogate data. Subsequently, we establish the almost complete uniform convergence rate of the estimator. To validate our results, we conduct experiments on both simulated data and a real dataset. Our results demonstrate the superiority of our estimator over traditional estimators when dealing with incomplete data. An application on simulated and then real data is provided.

Keywords: Almost complete convergence; Cumulative distribution function; Entropy; Functional data analysis; Small ball probability; Semi-metric space; Surrogate response; Spectrometric data (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-025-00989-1

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