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

<p>The main objective of this paper is to investigate the nonparametric estimation of the conditional density of a scalar response variable <italic>Y</italic>, given the explanatory variable <italic>X</italic> taking value in a Hilbert space when the sample of observations is considered as an independent random variables with identical distribution (i.i.d) and are linked with a single functional index structure. First of all, a kernel type estimator for the conditional density function (<italic>cond-df</italic>) is introduced. Afterwards, the asymptotic properties are stated for a conditional density estimator when the observations are linked with a single-index structure from which one derives a central limit theorem (CLT) of the conditional density estimator to show the asymptotic normality of the kernel estimate of this model. As an application the conditional mode in functional single-index model is presented, and the asymptotic (1 – ζ) confidence interval of the conditional mode function is given for 0 &lt; ζ &lt; 1. A 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.</p>
</abstract>

The main objective of this paper is to investigate the nonparametric estimation of the conditional density of a scalar response variable Y, given the explanatory variable X taking value in a Hilbert space when the sample of observations is considered as an independent random variables with identical distribution (i.i.d) and are linked with a single functional index structure. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated for a conditional density estimator when the observations are linked with a single-index structure from which one derives a central limit theorem (CLT) of the conditional density estimator to show the asymptotic normality of the kernel estimate of this model. As an application the conditional mode in functional single-index model is presented, and the asymptotic (1 – ζ) confidence interval of the conditional mode function is given for 0 < ζ < 1. A 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.

Asymptotic Normality of Conditional Density and Conditional Mode in the Functional Single Index Model

Statistics Laboratory Stochastic Processes

University Djillali LIABES of Sidi Bel Abbes

Econometrics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The main objective of this paper is to investigate the nonparametric estimation of the conditional density of a scalar response variable Y, given the...

Asymptotic Normality of Conditional Density and Conditional Mode in the Functional Single Index Model

Publié en ligne: 12 mai 2021

Pages: 1 - 24

DOI: https://doi.org/10.15611/eada.2021.1.01

Mots clés
asymptotic normality, conditional density, functional single index model, functional random variable, nonparametric estimation

© 2021 Fatima Akkal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Asymptotic Normality of Conditional Density and Conditional Mode in the Functional Single Index Model

Publié en ligne: 12 mai 2021

Pages: 1 - 24

DOI: https://doi.org/10.15611/eada.2021.1.01

Mots clésasymptotic normality, conditional density, functional single index model, functional random variable, nonparametric estimation

© 2021 Fatima Akkal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
asymptotic normality, conditional density, functional single index model, functional random variable, nonparametric estimation