Strong uniform consistency rates of conditional quantile estimation in the single functional index model under random censorship

Kadiri Nadia (), Rabhi Abbes () and Bouchentouf Amina Angelika ()
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Kadiri Nadia: Statistics Laboratory Stochastic Processes University Djillali LIABES of Sidi Bel Abbes,Sidi Bel Abbes, Algeria
Rabhi Abbes: Laboratory of Mathematics, University Djillali LIABES of Sidi Bel Abbes,Sidi Bel Abbes, Algeria
Bouchentouf Amina Angelika: Laboratory of Mathematics, University Djillali LIABES of Sidi Bel Abbes,Sidi Bel Abbes, Algeria

Dependence Modeling, 2018, vol. 6, issue 1, 197-227

Abstract: The main objective of this paper is to non-parametrically estimate the quantiles of a conditional distribution in the censorship model when the sample is considered as an -mixing sequence. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we estimate the quantiles by inverting this estimated cond-cdf and state the asymptotic properties when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. This approach can be applied in time series analysis.

Keywords: Conditional quantile; conditional cumulative distribution; derivatives of conditional cumulative distribution; functional data; kernel estimator; nonparametric estimation; probabilities of small balls; strong mixing processes (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:6:y:2018:i:1:p:197-227:n:13

DOI: 10.1515/demo-2018-0013

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