<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (<italic>cond-cdf</italic>) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated <italic>cond-cdf</italic>, the asymptotic properties are stated when the observations are linked with a single-index structure. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.</p>
</abstract>

The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.

Asymptotic Results of a Nonparametric Conditional Quantile Estimator in the Single Functional Index Modeling under Random Censorship

University Djillali LIABES of Sidi Bel Abbes

Faculty of Exact Sciences, Probability and Statistics

General Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the...

Asymptotic Results of a Nonparametric Conditional Quantile Estimator in the Single Functional Index Modeling under Random Censorship

Publié en ligne: 30 mars 2022

Pages: 137 - 168

Reçu: 04 oct. 2020

Accepté: 28 juil. 2021

DOI: https://doi.org/10.2478/gm-2021-0020

Mots clés
Conditional quantile, censored data, functional random variable, kernel estimator, nonparametric estimation, probabilities of small balls, single index model

© 2021 Nadia Kadiri et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Asymptotic Results of a Nonparametric Conditional Quantile Estimator in the Single Functional Index Modeling under Random Censorship

Publié en ligne: 30 mars 2022

Pages: 137 - 168

Reçu: 04 oct. 2020

Accepté: 28 juil. 2021

DOI: https://doi.org/10.2478/gm-2021-0020

Mots clésConditional quantile, censored data, functional random variable, kernel estimator, nonparametric estimation, probabilities of small balls, single index model

© 2021 Nadia Kadiri et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Conditional quantile, censored data, functional random variable, kernel estimator, nonparametric estimation, probabilities of small balls, single index model