Title:

Asymptotic normality of conditional density and conditional mode in the functional single index model

Group publication title:

Ekonometria = Econometrics

Title in english:

Asymptotyczna normalność rozkładu warunkowej gęstości i warunkowej dominanty modelu jednowskaźnikowego

Creator:

Akkal, Fatima ; Kadiri, Nadia ; Rahbi, Abbes

Subject and Keywords:

asymptotic normality ; conditional density ; functional single index model ; functional random variable ; nonparametric estimation ; asymptotyczna normalność ; gęstość warunkowa ; funkcjonalny model pojedynczego wskaźnika ; funkcjonalna zmienna losowa ; estymacja nieparametryczna

Description:

Econometrics = Ekonometria, 2021, Vol. 25, No. 1, s. 1-24

Abstrakt:

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 singleindex 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

Publisher:

Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu

Place of publication:

Wrocław

Date:

2021

Resource Type:

artykuł

Resource Identifier:

doi:10.15611/eada.2021.1.01

Language:

eng

Relation:

Econometrics = Ekonometria, 2021, Vol. 25, No. 1

Rights:

Pewne prawa zastrzeżone na rzecz Autorów i Wydawcy

Access Rights:

Dla wszystkich zgodnie z licencją

License:

CC BY-SA 4.0

Location:

Uniwersytet Ekonomiczny we Wrocławiu